Theorems of Perron-Frobenius type for matrices without sign restrictions
type: Item
instance of: scholarly article
title: Theorems of Perron-Frobenius type for matrices without sign restrictions
zbMATH Open document ID: 0901.15002
DOI: 10.1016/S0024-3795(96)00522-8
published in: Linear Algebra and its Applications
publication date: 1998-11-26T00:00:00Z
review text: For \(A\in M_n(R)\) the author defines the `sign-real spectral radius' \(\rho_0^S (A)= \max_{S\in {\mathcal S}} \rho_0 (SA)\), where \(S\) is an \(n\times n\) signature matrix (a diagonal matrix with diagonal entries 1 or \(-1)\) and \(\rho_0(A)\) is the real spectral radius (an absolutely largest real eigenvalue of \(A)\). He derives various properties, characterizations, and bounds of \(\rho_0^S (A)\); for instance, a behavior similar to that of the Perron eigenvalue of a nonnegative matrix. \(\rho_0^S(A)\) is closely related to the componentwise distance to the nearest singular matrix as well as to the Perron eigenvalue of the (entrywise) absolute value of \(A\) and to the \(\mu\)-number.
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 1083207
zbMATH Keywords: \(P\)-matrices
zbMATH Keywords: sign-real spectral radius
zbMATH Keywords: Perron eigenvalue
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: nearest singular matrix
author: Siegfried M. Rump
reviewed by: Erwin O. Kreyszig
describes a project that uses: mctoolbox
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1083207