Diagonalizing triangular matrices via orthogonal Pierce decompositions
type: Item
instance of: scholarly article
title: Diagonalizing triangular matrices via orthogonal Pierce decompositions
zbMATH Open document ID: 1074.15006
published in: Linear Algebra and its Applications
publication date: 2005-06-01T00:00:00Z
full work available at URL: http://hdl.handle.net/1822/1249
review text: Sufficient conditions are derived under which the sum \(m\) = \(a\) + \(b\) in a ring \(R\), with \(a\) regular, is equivalent to a sum \(n\) = \(e\)\(n\)\(f\) + (1 - \(e\))\(n\) (1 - \(f\)), which admits an orthogonal Pierce decomposition, for suitable idempotents \(e\) and \(f\). These results are used to show that a lower triangular matrix, with \(a\) regular diagonal, is equivalent to its diagonal iff the matrix admits a lower triangular von Neumann inverse.
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 2173159
zbMATH Keywords: rings
zbMATH Keywords: triangular matrices
zbMATH Keywords: von Neumann regularity
zbMATH Keywords: diagonalization
zbMATH Keywords: Pierce decomposition
zbMATH Keywords: von Neumann inverse
author: R. E. Hartwig
author: P. Patrício
author: R. Puystjens
MaRDI profile type: Publication
OpenAlex ID: W1967868901
cites work: The matrix equation \(AX-YB=C\)
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cites work: About the von Neumann regularity of triangular block matrices
DOI: 10.1016/J.LAA.2004.10.002
description: scientific article; zbMATH DE number 2173159