Generalized and hypergeneralized projectors
type: Item
instance of: scholarly article
title: Generalized and hypergeneralized projectors
zbMATH Open document ID: 0887.15024
DOI: 10.1016/S0024-3795(96)00541-1
author: Götz Trenkler
author: Jürgen Gross
published in: Linear Algebra and its Applications
publication date: 1997-10-20T00:00:00Z
review text: A complex \(n\times n\) matrix \(A\) satisfying \(A=A^3\), \(A=A^4\), \(A^2=A^*\) (conjugate transpose) or \(A^2=A^+\) (Moore-Penrose inverse) is called tripotent, quadripotent, generalized projector or hypergeneralized projector, respectively. The authors give a series of characterizations, e.g. for normal quadripotent and quadripotent matrices \(A\) satisfying range \(A=\) range \(A^*\). Conditions for the sum, difference and product of (hyper-)generalized projectors to be a mapping of the same kind are given.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1076307
zbMATH Keywords: quadripotent matrix
zbMATH Keywords: range
zbMATH Keywords: tripotent matrix
zbMATH Keywords: generalized projector
zbMATH Keywords: hypergeneralized projector
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1076307