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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In linear algebra, the Perron Frobenius theorem, named after Oskar Perron and Georg Frobenius, states results concerning the eigenvalues and eigenvectors of irreducible non-negative square matrices. It has important applications to probability theory (ergodicity of Markov chains) and the theory of dynamical systems (subshifts of finite type).