The pyramid decomposition and rank minimization
type: Item
instance of: scholarly article
title: The pyramid decomposition and rank minimization
zbMATH Open document ID: 0797.15013
DOI: 10.1016/0024-3795(93)90509-M
author: R. E. Hartwig
published in: Linear Algebra and its Applications
publication date: 1994-10-24T00:00:00Z
review text: The authors show that a general matrix \(M\) over a regular ring with unit admits a pyramid decomposition \(M=M_ 1 + M_ 2 + M_ 3 + M_ 4\) with \(M_ 1\leq M_ 1 + M_ 2 \leq M_ 1 + M_ 2 + M_ 3 \leq M\), where the so-called minus order \(A \leq B\) means that \(XA = XB\) and \(AY = BY\) for some inner inverses \(X\), \(Y\) of \(A\). In fact, there are many such decompositions derived from the Pierce decomposition of \(M\) relative to an arbitrary pair of idempotents.
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 459076
zbMATH Keywords: rank minimization
zbMATH Keywords: generalized inverse
zbMATH Keywords: regular ring
zbMATH Keywords: pyramid decomposition
zbMATH Keywords: minus order
zbMATH Keywords: inner inverses
zbMATH Keywords: Pierce decomposition
reviewed by: Jaroslav Zemánek
MaRDI profile type: Publication
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Wikidata QID: Q126377149
description: scientific article; zbMATH DE number 459076