In linear algebra, the **Perron–Frobenius theorem**, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector has strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices. This theorem has important applications to probability theory (ergodicity of Markov chains); to the theory of dynamical systems (subshifts of finite type); to economics (Leontief's input-output model); to demography (Leslie population age distribution model), to Internet search engines and even ranking of football teams

Read more about Perron–Frobenius Theorem: Statement of The Perron–Frobenius Theorem, Applications, Proof Methods, Caveats, Terminology

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**Perron–Frobenius Theorem**- Terminology

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“To insure the adoration of a *theorem* for any length of time, faith is not enough, a police force is needed as well.”

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