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Perron-Frobenius theorem |
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Perron-Frobenius theorem [pe′rōn frō′bā·nē·u̇s ‚thir·əm] (mathematics) IfMis a matrix with positive entries, then its largest eigenvalue λ is positive and simple; moreover, there exist vectorsvandwwith positive components such thatvM= λvandMw= λw, if the inner product ofvwithwis 1, then the limit of λ -ntimes thei,jth entry ofMnasngoes to infinity is the product of theith component ofwand thejth component ofv. How to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit webmaster's page for free fun content. |
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