Perron-frobenius theory for a generalized eigenproblem
نویسندگان
چکیده
منابع مشابه
Generalized Perron-Frobenius Theorem for Nonsquare Matrices
The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...
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We present an extension of Perron–Frobenius theory to the spectra and numerical ranges of Perron polynomials, namely, matrix polynomials of the form L(λ) = Iλ − Am−1λm−1 − · · · − A1λ− A0, where the coefficient matrices are entrywise nonnegative. Our approach relies on the companion matrix linearization. First, we recount the generalization of the Perron–Frobenius Theorem to Perron polynomials ...
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ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 1995
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081089508818429