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SEO Keyword summary for en.wikipedia.org/wiki/lanczos_algorithm
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be displaystyle
Focus keyword
Short and long tail
Short Tail Keywords displaystyle lambda lanczos |
long Tail Keywords (2 words) mdisplaystyle m lanczos algorithm sidebar hide vdisplaystyle v arbitrary vector |
long Tail Keywords (3 words) move to sidebar vector with euclidean euclidean norm 1displaystyle nndisplaystyle ntimes n convergence and other norm 1displaystyle 1 create account log |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/lanczos_algorithm page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
Title length
lanczos algorithm wikipedia
Meta description
Meta description legth
Meta description SEO
No meta relevance in the description detected !
Content SEO
Number of Words
Spam detected?
Headings
Heading distribution
Heading normalisation
Heading SEO impact
Emphasis (bold and italic)
Emphasis SEO impact
Images
Number of images
Images dimensions
Image alt descriptions
Images SEO impact
wikipedia free encyclopedia displaystyle ntimes vmapsto tvav mtimes avtv mathbb alpha dots beta jwj jneq vjwj wjavj jwjvj wjwjalpha jvjbeta jvj tbeginpmatrixalpha ddots malpha mendpmatrix avjwjbeta odn odmn lambda txlambda yvx beginalignedayavxvtvvxvtixvtxvlambda xlambda vxlambda yendaligned omlog mll neq jgeqslant auj vjj axin operatorname span dotsc xin leqslant vjuj gkjvkuj aujuj sum jgkjvk jgkjvkwj ujvjin avj hkjvkwj jhkjvk hkj avjsum hkjvk ujin ldots vkavjvkavjavkvj avkin javj vjoverline vjavj overline hjj hjjavjvjoverline vjavjoverline hvav hleftvavrightvavvavh rxfrac xaxxxqquad max min mathcal subset cdots xjyjin beginalignedrx geqslant endaligned nabla rxj ryj xxaxrxx axj ayj ljj azin zin zxj zyj ljoperatorname rxjmax ljrzqquad textandqquad ryjmin ljrz dotsb azklambda kzk dkzkv textstyle ndkzk varepsilon theta leftv right pav rpav frac apav paapav papav asum ndkzksum ndklambda qav ndkqlambda ndkplambda klambda kplambda kzkv kzklambda ndk ksum plambda kfrac kleftplambda kright leftplambda ckcos xcoskx pxcm leftfrac nlambda nright kgeqslant nsum nrightcm left rho reoperatorname arcosh sqrt beginalignedlambda nleft rightcm ptfrac nfrac cosh leftrm ptleqslant nleqslant approx uau uaulambda rapprox uapprox wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/lanczos_algorithm
Mobile rendering
Mobile optimizations
Responsive design detected (mobile css)
No flash detected !
Mobile improvement
Marketing / lead generation for en.wikipedia.org/wiki/lanczos_algorithm
Social Media
Facebook shares | Facebook likes | ||
Facebook comments | Tweets | ||
Google +1 |
Conversion form
Search form
Analytics
Online presence
SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
algorithm found in path !
lanczos found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
Favicon icon found?
Robots.txt found?
Sitemap found?
Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
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en.m.wikipedia.org |
en.wikipedia.org wikimedia foundation inc
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w view history
httpsenwikipediaorgwindexphptitlelanczosalgorithmoldid1223948364
page information
printable version
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wiki read
block lanczos algorithm
lanczos resampling
lanczos approximation
iterative method
cornelius lanczos
power iteration
eigenvalues and eigenvectors
hermitian matrix
numerical stability
orthonormal
continuant recursion
unitary
euclidean norm
eigenvalues
eigenvectors
diagonalization of a matrix
characteristic polynomial
divideandconquer eigenvalue algorithm
qr algorithm
power method
inverse iteration
caching
real
lossy compression
householder transformations
sparse problems
synchronisation
krylov subspaces
illconditioned
gramschmidt process
arnoldi iteration
threeterm recurrence relation
upper hessenberg
stationary points
rayleigh quotient
gradient
normal distribution
uniform distribution
chebyshev polynomials
eigengap
spectrum
arpack
peter montgomery
nullspace
gf2
latent semantic indexing
hits algorithm
jon kleinberg
pagerank
condensed matter physics
hamiltonians
strongly correlated electron systems
shell model
nuclear physics
nag library
matlab
gnu octave
scipy
graphlab
collaborative filtering
aiaa journal
bibcode
oclc
isbn
yousef saad
d calvetti
electronic transactions on numerical analysis
arxiv
s2cid
wayback machine
golub gene h
van loan charles f
ng andrew y
jordan michael i
numerical linear algebra
floating point
system of linear equations
matrix decompositions
matrix multiplication
algorithms
matrix splitting
cpu cache
cacheoblivious algorithm
multiprocessing
basic linear algebra subprograms blas
lapack
specialized libraries
general purpose software
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Links to external pages
Outloing links
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SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 87% | A title should reflect the contents of a site. This site has a 67 % match | |
Title Length | 30% | Limit your title to anywhere between 40 and 70 characters. Your title was 30 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 70% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 149 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 48% | Headers should reflect the contents of a site. This site has a 21 % match | |
Links | 10% | Link anchors should to some degree reflect the contents of a site. This site has a 5 % match | |
Image alt tags | 17% | Image alt tags should to some degree reflect the contents of a site. This site has a 6 % match | |
Bold and italic | 42% | Bold and italic tags should reflect the contents of a site to some degree. This site has a 14 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 99% | 99.445983379501 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 7264 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 83.64% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 732 inline style declarations ( <a style="color:green">) with a size of 25699 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
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en.wikipedia.org images and descriptions
218 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6732e27289d20a0d268a96d86baf1db153919e6c height: height attribute not set width: width attribute not set description: {\displaystyle u_{j+1}=u_{j+1}'/\|u_{j+1}'\|.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0 height: height attribute not set width: width attribute not set description: {\displaystyle j} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ffcb040e3c5c2a78e702a354bffe0bc16d172356 height: height attribute not set width: width attribute not set description: {\displaystyle \{v_{j}\}_{j=1}^{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a53b4e76242764d1bca004168353c380fef25258 height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {c} ^{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8d441086b42ae40610d1baac5e85558d90342171 height: height attribute not set width: width attribute not set description: {\displaystyle ax\in \operatorname {span} (v_{1},\dotsc ,v_{j+1})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4248836a9bf50046dd7bb30792e697403fa7e3e1 height: height attribute not set width: width attribute not set description: {\displaystyle x\in \operatorname {span} (v_{1},\dotsc ,v_{j})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dc9ed62d7bfb21cbf4ee4dcdf30814938ad7793b height: height attribute not set width: width attribute not set description: {\displaystyle 1\leqslant j |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/326d4c75412a9aae1d53034aeb3204f9d639547f height: height attribute not set width: width attribute not set description: {\displaystyle v_{j}=u_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3f9fb59f5261be394ff65b24f9d2a77c300d7a09 height: height attribute not set width: width attribute not set description: {\displaystyle u_{1},\dotsc ,u_{j-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/69b0c788a124a32684f109737f7cfab7611d6a58 height: height attribute not set width: width attribute not set description: {\displaystyle u_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5feb9c97e41fdf9610256837b95cc9853c915925 height: height attribute not set width: width attribute not set description: {\displaystyle v_{1}=u_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a73ca5f858a1bbd71eb567e2401759898d8a6ac6 height: height attribute not set width: width attribute not set description: {\displaystyle j=1,\dotsc ,m-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/db76bc62294101971f304984883dbadc7403c339 height: height attribute not set width: width attribute not set description: {\displaystyle u_{j+1}'=au_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9612cd0d3ef4231036aba152c0f1b8e6487d9545 height: height attribute not set width: width attribute not set description: {\displaystyle k=1,\dotsc ,j} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/64f46560fa19105bd2a7486d62a3efd905f9d04f height: height attribute not set width: width attribute not set description: {\displaystyle g_{k,j}=v_{k}^{*}u_{j+1}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ee3602f6902dddc93ead97eb6bc0c7f49fec1c74 height: height attribute not set width: width attribute not set description: {\displaystyle au_{j}=u_{j+1}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/717b29be4aba4fd4981c06d14e46c7e935280fd8 height: height attribute not set width: width attribute not set description: {\displaystyle v_{1},\dotsc ,v_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/38f56648308d6d6ecf9765e3ebf3f4995f3972ab height: height attribute not set width: width attribute not set description: {\displaystyle w_{j+1}=u_{j+1}'-\sum _{k=1}^{j}g_{k,j}v_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/91f344123c27ee03ab8c0680c149b6d8aacbf361 height: height attribute not set width: width attribute not set description: {\displaystyle u_{j+1}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/27a8a06bd6ad4fcf97048b6b38b5e774f85cf7b4 height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {span} (v_{1},\dotsc ,v_{j})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/177f442a08d8faf22ed23004a99810a95805e684 height: height attribute not set width: width attribute not set description: {\displaystyle w_{j+1}\neq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bbcba70f8b1834a5e5f99c3f5b8b78b18c069127 height: height attribute not set width: width attribute not set description: {\displaystyle u_{j+1}=u_{j+1}'/\|u_{j+1}'\|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a79871f47606edcd733a752874290add12a8132 height: height attribute not set width: width attribute not set description: {\displaystyle v_{j+1}=w_{j+1}/\|w_{j+1}\|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/44188b2fca1de82ae70cfd146d9fc6620042bf20 height: height attribute not set width: width attribute not set description: {\displaystyle u_{j+1}=v_{j+1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b670c7e0e7d0da6f02f5251397b88a37770a09a6 height: height attribute not set width: width attribute not set description: {\displaystyle au_{j}=\|u_{j+1}'\|u_{j+1}=u_{j+1}'=w_{j+1}+\sum _{k=1}^{j}g_{k,j}v_{k}=\|w_{j+1}\|v_{j+1}+\sum _{k=1}^{j}g_{k,j}v_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c8699384f3b0f2ff9220c2761be4dd4ebe05878f height: height attribute not set width: width attribute not set description: {\displaystyle u_{j}-v_{j}\in \operatorname {span} (v_{1},\dotsc ,v_{j-1})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d522447dcd637f280c9884481c0cda4d498a9e31 height: height attribute not set width: width attribute not set description: {\displaystyle w_{j+1}'=av_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/48ea6c8a18ca5c4c6e74e1fbc253d8556d75bd5d height: height attribute not set width: width attribute not set description: {\displaystyle h_{k,j}=v_{k}^{*}w_{j+1}'} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/15b4e9e3ea153e814f48eca05154ec9afa342a17 height: height attribute not set width: width attribute not set description: {\displaystyle w_{j+1}=w_{j+1}'-\sum _{k=1}^{j}h_{k,j}v_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0ee271f57c6e4dd4d515bf417380c38baa461430 height: height attribute not set width: width attribute not set description: {\displaystyle h_{j+1,j}=\|w_{j+1}\|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a5f6f757333624218d43daa74ac091488e34da9 height: height attribute not set width: width attribute not set description: {\displaystyle h_{j+1,j}\neq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/006a3dec2be5b3f4d71f2c36c12c87d8b4abeb8c height: height attribute not set width: width attribute not set description: {\displaystyle v_{j+1}=w_{j+1}/h_{j+1,j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e331ce871a0adfa09c9661c1d5caf9bb39068776 height: height attribute not set width: width attribute not set description: {\displaystyle h_{k,j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d50d39a2024d24df2932e073a36649663c0eda17 height: height attribute not set width: width attribute not set description: {\displaystyle av_{j}=\sum _{k=1}^{j+1}h_{k,j}v_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/10c6ae897e8577ca4ab7dc12f910a5dd5df18e25 height: height attribute not set width: width attribute not set description: {\displaystyle j |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c4828f9a739135081733d4c5b6522e51ca4e9b75 height: height attribute not set width: width attribute not set description: {\displaystyle v_{j+1}^{*}w_{j+1}'=v_{j+1}^{*}w_{j+1}=\|w_{j+1}\|v_{j+1}^{*}v_{j+1}=\|w_{j+1}\|.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0051806526fdca413dadf750203cf3b5f2a453a8 height: height attribute not set width: width attribute not set description: {\displaystyle u_{j}\in \operatorname {span} (v_{1},\ldots ,v_{j}),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8fce6a7c1a89932e6f6df2367197432cc944ef80 height: height attribute not set width: width attribute not set description: {\displaystyle u_{1},\ldots ,u_{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c98b2e8b693f05c2f6e935f65f07554d6f7f4e94 height: height attribute not set width: width attribute not set description: {\displaystyle h_{k,j}=v_{k}^{*}w_{j+1}'=v_{k}^{*}av_{j}=v_{k}^{*}a^{*}v_{j}=(av_{k})^{*}v_{j}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61b302e5bbd99af57faae834e3daef174d89e548 height: height attribute not set width: width attribute not set description: {\displaystyle k |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dfd48329fda0853a71b521a46f07065e7bc40b17 height: height attribute not set width: width attribute not set description: {\displaystyle av_{k}\in \operatorname {span} (v_{1},\ldots ,v_{j-1})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6d664760cc30da85edc6509fef16b6755caee655 height: height attribute not set width: width attribute not set description: {\displaystyle k=j-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65672f3d654a74f4b36f2751ee0c36088a8a9b01 height: height attribute not set width: width attribute not set description: {\displaystyle h_{j-1,j}=(av_{j-1})^{*}v_{j}={\overline {v_{j}^{*}av_{j-1}}}={\overline {h_{j,j-1}}}=h_{j,j-1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/962c91012062b0d61642fe75c6fec4863b5087d7 height: height attribute not set width: width attribute not set description: {\displaystyle k=j} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/491ada94eaaa0dc202a2cc32ba4bffe1af9d7513 height: height attribute not set width: width attribute not set description: {\displaystyle h_{j,j}=(av_{j})^{*}v_{j}={\overline {v_{j}^{*}av_{j}}}={\overline {h_{j,j}}},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4f87255ebbe8365adb9ceec34f33c02cb3121bc7 height: height attribute not set width: width attribute not set description: {\displaystyle v_{1},\ldots ,v_{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7eeeb9d1e7b54fa4ede90f8f7af000298f4daf23 height: height attribute not set width: width attribute not set description: {\displaystyle h=v^{*}av} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0787a191986af06b6509ae4cc1daba7e208a2db3 height: height attribute not set width: width attribute not set description: {\displaystyle h_{k,j}=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ac2349a70f6e89d239e891a0836afc1d2c449897 height: height attribute not set width: width attribute not set description: {\displaystyle k>j+1;} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b height: height attribute not set width: width attribute not set description: {\displaystyle h} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e198eca4af2fd58e953b59f5498dd5e620c80f38 height: height attribute not set width: width attribute not set description: {\displaystyle h^{*}=\left(v^{*}av\right)^{*}=v^{*}a^{*}v=v^{*}av=h} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4839039468716c80876dc904c9274d68fd3b0ea1 height: height attribute not set width: width attribute not set description: {\displaystyle r(x)={\frac {x^{*}ax}{x^{*}x}},\qquad x\in \mathbb {c} ^{n}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/957584ae6a35f9edf293cb486d7436fb5b75e803 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{\max }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/82c24522483ceaf1d54224b69af4244b60c3ac08 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{\min }} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9027196ecb178d598958555ea01c43157d83597c height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {l}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d height: height attribute not set width: width attribute not set description: {\displaystyle y} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/137f47c3123e3ab8b44e5cfd2844d51068158ea0 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {l}}_{1}\subset {\mathcal {l}}_{2}\subset \cdots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3bfc8b10a5ede4dae0d4341edcc65f6a20232e00 height: height attribute not set width: width attribute not set description: {\displaystyle x_{1},x_{2},\ldots } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/810d791818846f22d8fdca7f995f20aab142c15a height: height attribute not set width: width attribute not set description: {\displaystyle y_{1},y_{2},\dotsc } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af87e803dbc362a1e69a88602f6efe1f77fe4bed height: height attribute not set width: width attribute not set description: {\displaystyle x_{j},y_{j}\in {\mathcal {l}}_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f39fe00188889f8bc39137ef02d202228337d1df height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}r(x_{1})&\leqslant r(x_{2})\leqslant \cdots \leqslant \lambda _{\max }\\r(y_{1})&\geqslant r(y_{2})\geqslant \cdots \geqslant \lambda _{\min }\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5db47cb3d2f9496205a17a6856c91c1d3d363ccd height: height attribute not set width: width attribute not set description: {\displaystyle x_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f9fcfa47a24239277f549484c4175d361a9037a2 height: height attribute not set width: width attribute not set description: {\displaystyle \nabla r(x_{j})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f8df4e372390588acb968986cfc388e50b930b3a height: height attribute not set width: width attribute not set description: {\displaystyle y_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3a4a9107f195bc84dc31ff5b6ddf40af1054f880 height: height attribute not set width: width attribute not set description: {\displaystyle -\nabla r(y_{j})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/006b089725017228c859820b172bf6df9ca7457a height: height attribute not set width: width attribute not set description: {\displaystyle \nabla r(x)={\frac {2}{x^{*}x}}(ax-r(x)x),} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b624bcf5f21204fcac25fdbb1b58b2c2dde3aff7 height: height attribute not set width: width attribute not set description: {\displaystyle ax_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1a1439c374a941592af8a53e8e9814369e30b61f height: height attribute not set width: width attribute not set description: {\displaystyle ay_{j};} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4fbd414c1e6e987e21c550169dd5e7b64c12c475 height: height attribute not set width: width attribute not set description: {\displaystyle ay_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/61bee6d49c2a0ead1dad675746df49ca53c5c8ce height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {l}}_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/901fc910c19990d0dbaaefe4726ceb1a4e217a0f height: height attribute not set width: width attribute not set description: {\displaystyle 2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/43e79ac7e34dcc8d7532913f77051c8371f22f3d height: height attribute not set width: width attribute not set description: {\displaystyle \{{\mathcal {l}}_{j}\}_{j=1}^{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4221c3ca93b44047a8ce34aa31f7a1e85bed54df height: height attribute not set width: width attribute not set description: {\displaystyle az\in {\mathcal {l}}_{j+1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1539d9a8476b266be23777a28412462655cf22ed height: height attribute not set width: width attribute not set description: {\displaystyle z\in {\mathcal {l}}_{j},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/136920031ffeac31d88cc86f391d2913df2ce7bf height: height attribute not set width: width attribute not set description: {\displaystyle z=x_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f43d1047a97c34e1d843597368e2ad66f2cdfc6c height: height attribute not set width: width attribute not set description: {\displaystyle z=y_{j}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0b821c8801839e2265b80d03c77528353880a1cd height: height attribute not set width: width attribute not set description: {\displaystyle x_{1}=y_{1},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d69d12a58c9e8f2f3c6bcea252008c90aa85a200 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {l}}_{j}=\operatorname {span} (x_{1},ax_{1},\ldots ,a^{j-1}x_{1})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b5223a1d13ad515fb41c14495e6548b20b1ad6fa height: height attribute not set width: width attribute not set description: {\displaystyle r(x_{j})=\max _{z\in {\mathcal {l}}_{j}}r(z)\qquad {\text{and}}\qquad r(y_{j})=\min _{z\in {\mathcal {l}}_{j}}r(z).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9ecce0df8f88f42598e977d7dd9ff24f3f9ea033 height: height attribute not set width: width attribute not set description: {\displaystyle {\mathcal {l}}_{j},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/04d3bcf4016c43834610f94ba31ad1894ead4393 height: height attribute not set width: width attribute not set description: {\displaystyle \{v_{1},\ldots ,v_{j}\}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f8e36fe187f5c814ff13c1c318cc3a39b2d66c81 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}\geqslant \lambda _{2}\geqslant \dotsb \geqslant \lambda _{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/537f81a30f1a4e1592114b83b5c660a19490e018 height: height attribute not set width: width attribute not set description: {\displaystyle z_{1},\dotsc ,z_{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f8dac7f951be77ba0cee65a9c318396bc414e2d5 height: height attribute not set width: width attribute not set description: {\displaystyle az_{k}=\lambda _{k}z_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3bb5dd7f3f51d1527d26a66075244a8bda35e4b6 height: height attribute not set width: width attribute not set description: {\displaystyle k=1,\dotsc ,n} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/67228bb86a8e8e6b72c830ef52fb86b78077ea5f height: height attribute not set width: width attribute not set description: {\displaystyle d_{k}=z_{k}^{*}v_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e5dd5d9c3ce40a94c766608c41f99b9cec51bbb0 height: height attribute not set width: width attribute not set description: {\displaystyle \textstyle v_{1}=\sum _{k=1}^{n}d_{k}z_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2aae8864a3c1fec9585261791a809ddec1489950 height: height attribute not set width: width attribute not set description: {\displaystyle 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b78f5b2abc48e63b987b6d7527caa5aa9b1bb512 height: height attribute not set width: width attribute not set description: {\displaystyle d_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8389759f758f1e595fc6e4af997e2744345d684f height: height attribute not set width: width attribute not set description: {\displaystyle (d_{1},\dotsc ,d_{n})} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5a22036e7f2075ca8f566d2142710085ecae80f8 height: height attribute not set width: width attribute not set description: {\displaystyle |d_{1}|<\varepsilon } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0df93c8b59ec37d27b4084f9396198ff5c1ec09e height: height attribute not set width: width attribute not set description: {\displaystyle \theta _{1}\geqslant \theta _{2}\geqslant \dots \geqslant \theta _{m}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7f84b9443d095623e02fd287cd095123d70b0278 height: height attribute not set width: width attribute not set description: {\displaystyle \theta _{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/571a423bece8f29bcd1b48572f18dd4f6213dce2 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5adaa3619c27da284f8a29b49226b9cd4fd09bdf height: height attribute not set width: width attribute not set description: {\displaystyle \theta _{m}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/093ee22c3daf31b92ff5fa04ba0ce7862283e90c height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{n}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d3c462b1d2e680a7155a825096f686082aa7744 height: height attribute not set width: width attribute not set description: {\displaystyle \theta _{1},\ldots ,\theta _{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f91c55e0e557b8b72bf3cfbd4ce58fd980fbbbd2 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1},\ldots ,\lambda _{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0d457e88abd861f46ede37d27c4669c747367109 height: height attribute not set width: width attribute not set description: {\displaystyle r(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0370e52054a4ddcb753d34ec7eeff4115b90359f height: height attribute not set width: width attribute not set description: {\displaystyle \mathbb {c} ^{n},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/860e19905b781827f3fc504308972de017ce1c5f height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}\geqslant \theta _{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/129d9f3cd333fd6e1f3e5fd90946a3c805ac7914 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}-r(x)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bb17f49505c565eda688ffecf0cc04d72a2469be height: height attribute not set width: width attribute not set description: {\displaystyle \operatorname {span} \left\{v_{1},av_{1},a^{2}v_{1},\ldots ,a^{m-1}v_{1}\right\},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9e729122fbf50a608759ff9f72d31fd2d15010cb height: height attribute not set width: width attribute not set description: {\displaystyle p(a)v_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36 height: height attribute not set width: width attribute not set description: {\displaystyle p} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ecbbd201e0d8f1ccc91cb46362c4b72fa1bbe6c2 height: height attribute not set width: width attribute not set description: {\displaystyle m-1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7810e0d141cffdff492a023c93b627e7bf57f63a height: height attribute not set width: width attribute not set description: {\displaystyle v_{1},av_{1},a^{2}v_{1},\ldots ,a^{m-1}v_{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/180f741aa3ec0ac9e97e4777842b446c75bd4fa0 height: height attribute not set width: width attribute not set description: {\displaystyle p^{*}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa6fff7c9a59a271cb5dd2dc4a41aafddf28b07c height: height attribute not set width: width attribute not set description: {\displaystyle r(p(a)v_{1})={\frac {(p(a)v_{1})^{*}ap(a)v_{1}}{(p(a)v_{1})^{*}p(a)v_{1}}}={\frac {v_{1}^{*}p(a)^{*}ap(a)v_{1}}{v_{1}^{*}p(a)^{*}p(a)v_{1}}}={\frac {v_{1}^{*}p^{*}(a^{*})ap(a)v_{1}}{v_{1}^{*}p^{*}(a^{*})p(a)v_{1}}}={\frac {v_{1}^{*}p^{*}(a)ap(a)v_{1}}{v_{1}^{*}p^{*}(a)p(a)v_{1}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/22423cc066439702d36f289426538304499a7f9f height: height attribute not set width: width attribute not set description: {\displaystyle av_{1}=a\sum _{k=1}^{n}d_{k}z_{k}=\sum _{k=1}^{n}d_{k}\lambda _{k}z_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a187639d8de292b7ea6ef048cc64f3ddce0f5794 height: height attribute not set width: width attribute not set description: {\displaystyle q(a)v_{1}=\sum _{k=1}^{n}d_{k}q(\lambda _{k})z_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/06809d64fa7c817ffc7e323f85997f783dbdf71d height: height attribute not set width: width attribute not set description: {\displaystyle q} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5669ade7fdac65aafd94418f27ef40b94096bbce height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}-r(p(a)v_{1})=\lambda _{1}-{\frac {v_{1}^{*}\sum _{k=1}^{n}d_{k}p^{*}(\lambda _{k})\lambda _{k}p(\lambda _{k})z_{k}}{v_{1}^{*}\sum _{k=1}^{n}d_{k}p^{*}(\lambda _{k})p(\lambda _{k})z_{k}}}=\lambda _{1}-{\frac {\sum _{k=1}^{n}|d_{k}|^{2}\lambda _{k}p(\lambda _{k})^{*}p(\lambda _{k})}{\sum _{k=1}^{n}|d_{k}|^{2}p(\lambda _{k})^{*}p(\lambda _{k})}}={\frac {\sum _{k=1}^{n}|d_{k}|^{2}(\lambda _{1}-\lambda _{k})\left|p(\lambda _{k})\right|^{2}}{\sum _{k=1}^{n}|d_{k}|^{2}\left|p(\lambda _{k})\right|^{2}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6c035ffa69b5bca8bf2d16c3da3aaad79a8bcbfa height: height attribute not set width: width attribute not set description: {\displaystyle k=1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/80ade48438305c663290c92812a929b288d55a39 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}-\theta _{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3d2f8052630e67b00d04e3487e1d68ed7070470b height: height attribute not set width: width attribute not set description: {\displaystyle c_{k}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c3c9a2c7b599b37105512c5d570edc034056dd40 height: height attribute not set width: width attribute not set description: {\displaystyle k} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/acd23b73d88a33556e5a2cac14eac0167943af1b height: height attribute not set width: width attribute not set description: {\displaystyle c_{k}(\cos x)=\cos(kx)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/51e3b7f14a6f70e614728c583409a0b9a8b9de01 height: height attribute not set width: width attribute not set description: {\displaystyle [-1,1]} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a4ccfb29dab0a6153bec3fdb61360f923d9093b6 height: height attribute not set width: width attribute not set description: {\displaystyle p(x)=c_{m-1}\left({\frac {2x-\lambda _{2}-\lambda _{n}}{\lambda _{2}-\lambda _{n}}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5880a85b6793b39a8a575405a1ecf080736c2c76 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{2}=\lambda _{1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/801f857670585e77a5d9644a5636c5549a528232 height: height attribute not set width: width attribute not set description: {\displaystyle |p(\lambda _{k})|^{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5416cbab88065daf82832964f91d6b399ab8e6fd height: height attribute not set width: width attribute not set description: {\displaystyle k\geqslant 2} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/18214588406d9ca8d73c096c88a6ffa9cdc7d4d1 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}-\theta _{1}\leqslant \lambda _{1}-r(p(a)v_{1})={\frac {\sum _{k=2}^{n}|d_{k}|^{2}(\lambda _{1}-\lambda _{k})|p(\lambda _{k})|^{2}}{\sum _{k=1}^{n}|d_{k}|^{2}|p(\lambda _{k})|^{2}}}\leqslant {\frac {\sum _{k=2}^{n}|d_{k}|^{2}(\lambda _{1}-\lambda _{k})}{|d_{1}|^{2}|p(\lambda _{1})|^{2}}}\leqslant {\frac {(\lambda _{1}-\lambda _{n})\sum _{k=2}^{n}|d_{k}|^{2}}{|p(\lambda _{1})|^{2}|d_{1}|^{2}}}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d4f729fc798b0723774686d38edbc246f89d8d75 height: height attribute not set width: width attribute not set description: {\displaystyle p(\lambda _{1})=c_{m-1}\left({\frac {2\lambda _{1}-\lambda _{2}-\lambda _{n}}{\lambda _{2}-\lambda _{n}}}\right)=c_{m-1}\left(2{\frac {\lambda _{1}-\lambda _{2}}{\lambda _{2}-\lambda _{n}}}+1\right);} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/82dba35eb27fdbf7f9a19a7ab26f0f3b8a81f372 height: height attribute not set width: width attribute not set description: {\displaystyle \rho ={\frac {\lambda _{1}-\lambda _{2}}{\lambda _{2}-\lambda _{n}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b3ee766dbeb045b690f5642a5527dcc3001d23b5 height: height attribute not set width: width attribute not set description: {\displaystyle r=e^{\operatorname {arcosh} (1+2\rho )}=1+2\rho +2{\sqrt {\rho ^{2}+\rho }},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2a971e473f56e04b8e556a5085f49a1025a08878 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\lambda _{1}-\theta _{1}&\leqslant {\frac {(\lambda _{1}-\lambda _{n})\left(1-|d_{1}|^{2}\right)}{c_{m-1}(2\rho +1)^{2}|d_{1}|^{2}}}\\[6pt]&={\frac {1-|d_{1}|^{2}}{|d_{1}|^{2}}}(\lambda _{1}-\lambda _{n}){\frac {1}{\cosh ^{2}((m-1)\operatorname {arcosh} (1+2\rho ))}}\\[6pt]&={\frac {1-|d_{1}|^{2}}{|d_{1}|^{2}}}(\lambda _{1}-\lambda _{n}){\frac {4}{\left(r^{m-1}+r^{-(m-1)}\right)^{2}}}\\[6pt]&\leqslant 4{\frac {1-|d_{1}|^{2}}{|d_{1}|^{2}}}(\lambda _{1}-\lambda _{n})r^{-2(m-1)}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33 height: height attribute not set width: width attribute not set description: {\displaystyle r} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5cac28d03a3b254feb0e34bd25998174bf231f03 height: height attribute not set width: width attribute not set description: {\displaystyle r^{-2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64 height: height attribute not set width: width attribute not set description: {\displaystyle \rho } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8a544208e11603f9b36b178728154c951b3a7129 height: height attribute not set width: width attribute not set description: {\displaystyle |\lambda _{n}|\leqslant |\lambda _{2}|} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6b668a1bd1e8ab9452ca975b7497546e7c1ba187 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d6d2edacaa55460b6c364c2f8913517fc447ca6 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{n}=-\lambda _{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a3a5b47ba1df061a54312d7712efd7b2cd19510a height: height attribute not set width: width attribute not set description: {\displaystyle u=(1-t^{2})^{1/2}z_{1}+tz_{2}\approx z_{1}+tz_{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5abf655fa14f7ea44ad0ca781b59ff59c5f49117 height: height attribute not set width: width attribute not set description: {\displaystyle z_{2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/65658b7b223af9e1acc877d848888ecdb4466560 height: height attribute not set width: width attribute not set description: {\displaystyle t} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/62296f33b804772747d3ecf9c0bd9379e214c6b3 height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {\lambda _{2}}{\lambda _{1}}}={\frac {\lambda _{2}}{\lambda _{2}+(\lambda _{1}-\lambda _{2})}}={\frac {1}{1+{\frac {\lambda _{1}-\lambda _{2}}{\lambda _{2}}}}}={\frac {1}{1+2\rho }}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/84580bc851b19ea55fed8dc5209fde93c4156750 height: height attribute not set width: width attribute not set description: {\displaystyle u^{*}au=(1-t^{2})\lambda _{1}+t^{2}\lambda _{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/16daa06cb5a76df53fc9868aa777b93bf8a21d26 height: height attribute not set width: width attribute not set description: {\displaystyle \lambda _{1}-u^{*}au=(\lambda _{1}-\lambda _{2})t^{2},} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f76439c4642e0a55c5bea5a665f442bef3f312e height: height attribute not set width: width attribute not set description: {\displaystyle (1+2\rho )^{-2}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0d6d5abf2eff75045e8f588b7ce9d163484eeb height: height attribute not set width: width attribute not set description: {\displaystyle 1+2\rho } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/705d7f57ea37738841774e6c1affde418341d911 height: height attribute not set width: width attribute not set description: {\displaystyle r=1+2\rho +2{\sqrt {\rho ^{2}+\rho }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/361e75aeb737f2cb15d0ec4fdda9ab8103426792 height: height attribute not set width: width attribute not set description: {\displaystyle \rho \gg 1} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/39300c00e409b2ea0f387e226468b10771b99d78 height: height attribute not set width: width attribute not set description: {\displaystyle 1+4\rho } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cf6c6c26df1cdd92fd168a73c185bfe9cd54a773 height: height attribute not set width: width attribute not set description: {\displaystyle \rho \ll 1,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6cee739fd141aa13cf098730b41322b5e2d75bd3 height: height attribute not set width: width attribute not set description: {\displaystyle r\approx 1+2{\sqrt {\rho }}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ccb7dffa0b8ea44d8d0ab69f7123b57cd050392e height: height attribute not set width: width attribute not set description: {\displaystyle v_{1},v_{2},\cdots ,v_{m+1}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c6aaf5ce10d6add44b973e28fb3d95f37abf3721 height: height attribute not set width: width attribute not set description: {\displaystyle a\,} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/ecc50bf9677cbf980807dde3ef22ab1b90d4c313 height: height attribute not set width: width attribute not set description: {\displaystyle u\approx z_{1}+tz_{2}} |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://en.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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