A further algebraic version of Cochran's theorem and matrix partial orderings
type: Item
instance of: scholarly article
title: A further algebraic version of Cochran's theorem and matrix partial orderings
zbMATH Open document ID: 0696.15005
DOI: 10.1016/0024-3795(90)90341-9
author: Jerzy K. Baksalary
author: Jan Hauke
published in: Linear Algebra and its Applications
publication date: 1990-01-01T00:00:00Z
review text: The authors consider complex \(p\times q\) matrices \(A_ 1,A_ 2,...,A_ k\) and give a set of necessary and sufficient conditions implying that (i) for \(i=1,2,...,k\) \(P_ i=A_ iA^*_ i\) and \(Q_ i=A^*_ iA_ i\) are Hermitian projections such that \(P_ iA_ j=A_ jQ_ i=\delta_{ij}A_ j\) for \(j=1,2,...,k\), and (ii) \(P=P_ 1+P_ 2+...+P_ k\) and \(Q=Q_ 1+Q_ 2+...+Q_ k\) are Hermitian projections such that \(PA=AQ\) where \(A=A_ 1+A_ 2+....+A_ k\). A new partial ordering for \(p\times q\) complex matrices in terms of their generalized inverses is also given in the paper.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 4139936
zbMATH Keywords: Cochran's theorem
zbMATH Keywords: star partial ordering
zbMATH Keywords: minus partial ordering
zbMATH Keywords: space preordering
zbMATH Keywords: Hermitian projections
zbMATH Keywords: generalized inverses
reviewed by: László Mihályffy
MaRDI profile type: Publication
full work available at URL: 0024-3795(90)90341-9
OpenAlex ID: W2009303063
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description: scientific article; zbMATH DE number 4139936