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Main Title: The Frobenius-Jordan form of nonnegative matrices
Author(s): Mehrmann, Volker
Saha, Manideepa
Type: Research Paper
Abstract: In this paper we use preferred and quasi-preferred bases of generalized eigenspaces associated with the spectral radius of nonnegative matrices to analyze the existence and uniqueness of a variant of the Jordan canonical form which we call Frobenius-Jordan form. It is a combination of the classical Jordan canonical form in the part associated with the eigenvalues that are different from the spectral radius, while it is like the Frobenius normal form in the part associated with the spectral radius. Based on the Frobenius-Jordan form, spectral and combinatorial properties of nonnegative matrices are discussed. In particular, we analyze the existence of nonnegative graph representations of the generalized eigenspace associated with the spectral radius.
Subject(s): preferred basis
quasi-preferred basis
Frobenius-Jordan form
Issue Date: 21-Jun-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 15A48 Positive matrices and their generalizations; cones of matrices
15A21 Canonical forms, reductions, classification
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 21
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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