Maps on spaces of symmetric matrices preserving idempotence
type: Item
instance of: scholarly article
title: Maps on spaces of symmetric matrices preserving idempotence
zbMATH Open document ID: 1111.15003
author: Yu Qiu Sheng
author: Baodong Zheng
author: Xian Zhang
published in: Linear Algebra and its Applications
publication date: 2007-01-09T00:00:00Z
review text: The authors classify maps on \(n\)-by--\(n\) symmetric matrices, over rather general fields, with the property that \(A-\lambda B\) is idempotent precisely when \(\Phi(A)-\lambda\Phi(B)\) is. No linearity nor surjectivity/injectivity of \(\Phi\) is part of the hypothesis. It is assumed that \(n\geq 4\), the underlying field has at least \(5\) elements, and that its characteristics differs from \(2\).
reviewed by: Bojan Kuzma
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 5083626
zbMATH Keywords: Field
zbMATH Keywords: Idempotence preserver
zbMATH Keywords: Symmetric matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2006.08.012
OpenAlex ID: W2032364921
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DOI: 10.1016/J.LAA.2006.08.012
description: scientific article; zbMATH DE number 5083626