Automorphisms of \(M_{n}\), partially ordered by rank subtractivity ordering
type: Item
instance of: scholarly article
title: Automorphisms of \(M_{n}\), partially ordered by rank subtractivity ordering
zbMATH Open document ID: 1080.15017
author: Peter Legiša
published in: Linear Algebra and its Applications
publication date: 2004-11-22T00:00:00Z
review text: Let \(M_n\) be the space of all \(n{\times}n\) matrices with coefficients in \(\mathbb{R}\) or \(\mathbb{C}\), where \(n\geqslant 3\). The rank subtractivity or minus partial order on \(M_n\) is defined by \(A\leqslant_{{\text{rs}}}B\) iff \({\text{rank}}\,B = {\text{rank}}\,A+{\text{rank}}\,(B-A)\). This order, restricted to idempotents, induces the usual order on idempotents, i.e. \(P={P^2}_{{\text{rs}}}\,Q=Q^2\) iff \(PQ=QP=P\). The author characterizes bijective mappings \(\Phi\) on \(M_n\) such that \(A\leqslant_{{\text{rs}}}B\) iff \(\Phi(A)\leqslant_{{\text{rs}}}\Phi(B), \; (A,B \in M_n)\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 2117288
zbMATH Keywords: space of all \(n{\times}n\) matrices
zbMATH Keywords: minus partial order
zbMATH Keywords: poset
zbMATH Keywords: full matrix algebra
zbMATH Keywords: automorphism
zbMATH Keywords: rank subtractivity
reviewed by: Nikolai I. Osetinski
MaRDI profile type: Publication
full work available at URL: j.laa.2004.03.024
OpenAlex ID: W2011706026
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DOI: 10.1016/J.LAA.2004.03.024
description: scientific article; zbMATH DE number 2117288