The Perron-Frobenius Theorem Revisited |
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Authors: | Radjavi Heydar |
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Affiliation: | (1) Department of Mathematics, Statistics & Computing Science, Dalhousie University, Halifax, Nova Scotia, B3H 3J5 (Fax |
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Abstract: | An extension of the Perron-Frobenius Theorem is presented in the much more general setting of indecomposable semigroups of nonnegative matrices. Many features of the original theorem including the existence of a fixed positive vector, a block-monomial form, and spectral stability properties hold simultaneously for these semigroups. The paper is largely self-contained and the proofs are elementary. The classical theorem and some related results follow as corollaries. |
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Keywords: | indecomposable fixed vector matrix semigroup nonnegative Perron– Frobenius |
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