Generalized eigenvectors and sets of nonnegative matrices
نویسندگان
چکیده
منابع مشابه
Matrix functions preserving sets of generalized nonnegative matrices
Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n×n real eventually positive matrices; and WPFn, the set of matrices A ∈ R such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n× n real eventually nonnegative ...
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Matrix functions preserving several sets of generalized nonnegative matrices are characterized. These sets include PFn, the set of n×n real eventually positive matrices; and WPFn, the set of matrices A ∈ R such that A and its transpose have the Perron-Frobenius property. Necessary conditions and sufficient conditions for a matrix function to preserve the set of n× n real eventually nonnegative ...
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We consider maps fK(v) = minA∈K Av and gK(v) = maxA∈KAv, where K is a finite set of nonnegative matrices and by “min” and “max” we mean component-wise minimum and maximum. We transfer known results about properties of gK to fK. In particular we show existence of nonnegative generalized eigenvectors of fK, give necessary and sufficient conditions for existence of strictly positive eigenvector of...
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A set of nonnegative matricesM = {M1,M2, . . . ,Mk} is called primitive if there exist indices i1, i2, . . . , im such that Mi1Mi2 . . .Mim is positive (i.e. has all its entries > 0). The length of the shortest such product is called the exponent ofM. The concept of primitive sets of matrices comes up in a number of problems within control theory, non-homogeneous Markov chains, automata theory ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1984
ISSN: 0024-3795
DOI: 10.1016/0024-3795(84)90161-7