Linear/additive preservers of rank 2 on spaces of alternate matrices over fields
type: Item
instance of: scholarly article
title: Linear/additive preservers of rank 2 on spaces of alternate matrices over fields
zbMATH Open document ID: 1075.15009
author: Xian Zhang
published in: Linear Algebra and its Applications
publication date: 2005-02-22T00:00:00Z
review text: A matrix \(A\in M_n(F)\) is said to be alternate if \(x^tAx=0\) for every \(x\in M_{n,1}(F)\). If the characteristic of \(F\) is not 2, \(A\) is alternate iff \(A\) is skew-symmetric, and if \(\text{char}(F)=2\), \(A\) is alternate iff it is symmetric. The author obtains a characterization of additive transformations on the space of alternate matrices which preserve the set of rank-2 matrices on the fields which are not isomorphic to their proper subfields. The characterization of the corresponding linear transformations is given for an arbitrary field.
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 2136673
zbMATH Keywords: alternate matrices
zbMATH Keywords: rank
zbMATH Keywords: field
zbMATH Keywords: linear preserver
zbMATH Keywords: additive preserver
reviewed by: Alexander Guterman
MaRDI profile type: Publication
full work available at URL: j.laa.2004.08.028
OpenAlex ID: W2033011253
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DOI: 10.1016/J.LAA.2004.08.028
description: scientific article; zbMATH DE number 2136673