Idempotency of the Hermitian part of a complex matrix
type: Item
instance of: scholarly article
title: Idempotency of the Hermitian part of a complex matrix
zbMATH Open document ID: 0945.15014
DOI: 10.1016/S0024-3795(97)10045-3
author: Jürgen Gross
published in: Linear Algebra and its Applications
publication date: 2000-10-03T00:00:00Z
review text: The paper characterizes matrices \(A\) with the Hermitian part, \(H(A)= (A + A^*)/2,\) being idempotent. It is shown that such matrices belong to the class of complex \(m\times m\) matrices for which \(A A^+ = A^+ A,\) where \(A^+\) is the Moore-Penrose inverse of \(A\), or equivalently, the range of \(A\) equals the range of \(A^*\).
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A60
zbMATH DE Number: 1331295
zbMATH Keywords: orthogonal projector
zbMATH Keywords: idempotency
zbMATH Keywords: Hermitian part
zbMATH Keywords: normality
zbMATH Keywords: EP matrix
zbMATH Keywords: Moore-Penrose inverse
reviewed by: Arbind Kumar Lal
MaRDI profile type: Publication
cites work: Powers of matrices and idempotency
cites work: Q4002321
cites work: Matrix Analysis
cites work: Q3207128
cites work: Lattice properties of the *-order for complex matrices
cites work: Q4323492
Wikidata QID: Q126531603
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description: scientific article; zbMATH DE number 1331295