Equalities for orthogonal projectors and their operations
type: Item
instance of: scholarly article
title: Equalities for orthogonal projectors and their operations
zbMATH Open document ID: 1223.15010
author: Yongge Tian
published in: Central European Journal of Mathematics
publication date: 2011-05-27T00:00:00Z
review text: A complex square matrix \(A\) is called an orthogonal projector if \(A^{2} = A = A^{*}\), where \(A^{*}\) denotes the conjugate transpose of \(A\). The author gives a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. He first collects some well-known rank formulas for orthogonal projectors and their operations, and then gives various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, some necessary and sufficient conditions are given for various equalities for orthogonal projectors and their operations to hold.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 15B10
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 5900619
zbMATH Keywords: orthogonal projector
zbMATH Keywords: idempotent matrix
zbMATH Keywords: matrix equality
zbMATH Keywords: rank equality
zbMATH Keywords: range equality
zbMATH Keywords: commutativity
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: group inverse
zbMATH Keywords: reverse-order law
MaRDI profile type: Publication
full work available at URL: s11533-010-0057-9
OpenAlex ID: W2064215274
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DOI: 10.2478/S11533-010-0057-9
description: scientific article; zbMATH DE number 5900619