The difference and sum of projectors
type: Item
instance of: scholarly article
title: The difference and sum of projectors
zbMATH Open document ID: 1060.15011
author: J. J. Koliha
author: I. Straškraba
author: Vladimir Rakočević
published in: Linear Algebra and its Applications
publication date: 2004-10-04T00:00:00Z
review text: The authors give simple proofs, without reference to rank theory for matrices, of some results on the non-singularity of the difference \(P-Q\) of projections \(P\) and \(Q\) obtained by \textit{J. Gross } and \textit{G. Trenkler} [SIAM J. Matrix Anal. Appl. 21, No. 2, 390--395 (1999; Zbl 0946.15020)]. In the proofs, the relations among the ranges and the null-spaces of projections \(P\) and \(Q\) have been employed. A new characterization of the non-singularity of \(P-Q\) in terms of the non-singularity of \(P+Q\) has been obtained. The authors also give necessary and sufficient conditions for the non-singularity of \(P+Q\) and explicit formulae for the inverse of \(P+Q\) separately in the case when \(P-Q\) is non-singular, and when \(P-Q\) is singular.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 2105747
zbMATH Keywords: projector
zbMATH Keywords: direct sum
zbMATH Keywords: inverse
zbMATH Keywords: non-singularity
MaRDI profile type: Publication
full work available at URL: j.laa.2004.03.008
OpenAlex ID: W1999485964
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DOI: 10.1016/J.LAA.2004.03.008
description: scientific article; zbMATH DE number 2105747