Oblique projectors and group involutory matrices
type: Item
instance of: scholarly article
title: Oblique projectors and group involutory matrices
zbMATH Open document ID: 1030.15023
DOI: 10.1016/S0096-3003(02)00249-7
author: C. Coll
author: Néstor Thome
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: A square complex matrix \(P\) is called an oblique projector if \(P^2=P\). If a square complex matrix \(X\) satisfies the conditions \(AXA=A\), \(XAX=X\) and \(AX=XA\), then it is called the group inverse of a square complex matrix \(A\). For the complex matrix \(A\), the group involutory matrices are defined as those square matrices \(A\) that coincide with its group inverse \(A^{\#}\), i.e. \(A^{\#}=A\). Conditions characterizing the group involutory matrix as the sum of two projectors are given. Next, the conditions defining when a linear combination of projectors is a group involutory matrix are presented and proved. An application of projectors to the solution of a feedback control problem is discussed and an example of a state-space descriptor control linear system is analyzed.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 1978100
zbMATH Keywords: projector
zbMATH Keywords: group inverse
zbMATH Keywords: group involutory matrix
zbMATH Keywords: feedback control problem
MaRDI profile type: Publication
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cites work: Q4061081
cites work: Group inverse and group involutory Matrices∗
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cites work: Q5623132
cites work: On the perturbation of the group inverse and oblique projection
full work available at URL: s0096-3003(02)00249-7
OpenAlex ID: W2121474135
description: scientific article; zbMATH DE number 1978100