Multiplicative maps on matrices that preserve the spectrum
type: Item
instance of: scholarly article
title: Multiplicative maps on matrices that preserve the spectrum
zbMATH Open document ID: 0815.15009
DOI: 10.1016/0024-3795(94)90409-X
author: Scott H. Hochwald
published in: Linear Algebra and its Applications
publication date: 1995-07-09T00:00:00Z
review text: Soit \(M_ n\) l'ensemble des matrices \(n \times n\) sur l'ensemble des nombres complexes \((n \geq 2)\). Soit \(A_ n \subseteq M_ n\) l'ensemble des matrices inversibles, ou l'ensemble des matrices unitaires, ou un semi-groupe contenant les matrices singulières. Alors, pour une application \(\varphi\) particulière: \(A_ n \to M_ n\), il existe une matrice \(R\) de \(M_ n\) telle que \(\varphi (S) = R^{-1}SR\) pour tout \(S\) dans \(A_ n\).
reviewed by: F.Ribière Michaud
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 720482
zbMATH Keywords: multiplicative maps on matrices
zbMATH Keywords: invertible matrices
zbMATH Keywords: unitary matrices
zbMATH Keywords: spectrum preserving transformations
MaRDI profile type: Publication
cites work: Q3254327
cites work: Matrix Analysis
cites work: Q4040931
cites work: Spectrum-preserving linear maps
cites work: Q5568305
cites work: On tridiagonalization of matrices
cites work: Spectrum-preserving additive maps
cites work: A Decomposition of Orthogonal Transformations
cites work: The operator factorization problems
full work available at URL: 0024-3795(94)90409-x
OpenAlex ID: W2062899136
description: scientific article; zbMATH DE number 720482