Linear maps preserving Drazin inverses of matrices over fields
type: Item
instance of: scholarly article
title: Linear maps preserving Drazin inverses of matrices over fields
zbMATH Open document ID: 1075.15006
author: Changjiang Bu
published in: Linear Algebra and its Applications
publication date: 2005-02-22T00:00:00Z
review text: For a matrix \(A\in M_{n}(F)\) a matrix \(A^D\in M_{n}(F)\) is called the Drazin inverse of \(A\) if \(A^D\) is a solution of the equations: \[ AX=XA,\;XAX=X, \;A^kXA=A^k . \] The characterization of linear maps \(T\) from \(M_{n}(F)\) to \(M_{m}(F)\)preserving Drazin inverses of matrices (namely, \(T(A^D)=(T(A))^D\)) is obtained. Here \(F\) is constrained to be a field with at least 5 elements of characteristic different from 2. In the case \(char(F)=2\) and \(m=n\) the author described the linear bijections which preserves the Drazin inverses of matrices.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 2136676
zbMATH Keywords: linear preservers
zbMATH Keywords: field
zbMATH Keywords: Drazin inverse
reviewed by: Alexander Guterman
MaRDI profile type: Publication
full work available at URL: j.laa.2004.09.012
OpenAlex ID: W2052207306
cites work: Q2784581
cites work: Linear preserver problems: A brief introduction and some special techniques
cites work: Additive operators preserving idempotent matrices over fields and applications
cites work: Additive maps preserving M-P inverses of matrices over Fields∗
cites work: Q5704987
cites work: Linear maps preserving idempotence on matrix modules over principal ideal domains
DOI: 10.1016/J.LAA.2004.09.012
description: scientific article; zbMATH DE number 2136676