Matrix roots of eventually positive matrices
نویسندگان
چکیده
منابع مشابه
Eventually Nonnegative Matrices and their Sign Patterns
A matrix A ∈ Rn×n is eventually nonnegative (respectively, eventually positive) if there exists a positive integer k0 such that for all k ≥ k0, A ≥ 0 (respectively, A > 0). Here inequalities are entrywise and all matrices are real and square. An eigenvalue of A is dominant if its magnitude is equal to the spectral radius of A. A matrix A has the strong Perron-Frobenius property if A has a uniqu...
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It is a well-know fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive s...
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A sign pattern is a matrix whose entries belong to the set {+,−, 0}. An n-by-n sign pattern A is said to allow an eventually positive matrix if there exist some real matrices A with the same sign pattern as A and a positive integer k0 such that A > 0 for all k ≥ k0. It is well known that identifying and classifying the n-by-n sign patterns that allow an eventually positive matrix are posed as t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.10.052