Triple reverse-order law for weighted generalized inverses
type: Item
instance of: scholarly article
title: Triple reverse-order law for weighted generalized inverses
zbMATH Open document ID: 1031.15005
DOI: 10.1016/S0096-3003(00)00122-3
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: \textit{R. E. Hartwig} [Linear Algebra Appl. 76, 241-246 (1986; Zbl 0584.15002)] established the triple reverse-order law for Moore-Penrose inverses involving the computation of some Moore-Penrose inverses. For a given complex matrix \(A\) of size \(m \times n\), the weighted Moore-Penrose is the unique complex matrix \(X\) of size \(n \times m\) satisfying \(AXA=A\), \(XAX=X\) and \(MAX\) and \(NXA\) are Hermitian where \(M\) and \(N\) are Hermitian positive definite. The results found in this work extend the known cases. The problem studied is when the weighted Moore-Penrose of a triple product coincides with the product of the corresponding weighted Moore-Penrose of each one of the matrices in the reverse order. The obtained conditions do not involve any computation of Moore-Penrose inverses but only some ranks of certain matrices. In addition, some special cases are derived.
reviewed by: Néstor Thome
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1860991
zbMATH Keywords: Moore-Penrose inverses
zbMATH Keywords: weighted generalized inverse
zbMATH Keywords: reverse-order law
zbMATH Keywords: matrix computation
author: Wenyu Sun
author: Yimin Wei
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1860991