Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
type: Item
instance of: scholarly article
title: Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
zbMATH Open document ID: 0984.15011
DOI: 10.1016/S0024-3795(00)00033-1
published in: Linear Algebra and its Applications
publication date: 2002-05-07T00:00:00Z
review text: The author establishes a general Hermitian nonnegative-definite solution to the matrix equation \(A\times A^*=B\) \((A^*\) is the conjugate transpose of a complex matrix \(A)\) in a form which can be viewed as a corrected version of that derived by \textit{C. G. Khatri} and \textit{S. K. Mitra} [SIAM J. Appl. Math. 31, 579-585 (1976; Zbl 0359.65033)], and alternative version to that derived by \textit{J. K. Baksalary} [Linear Multilinear Algebra 16, 133-139 (1984; Zbl 0552.15009)]. By using the new representation he obtains solutions of minimal and maximal rank, respectively.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1563483
zbMATH Keywords: generalized inverse
zbMATH Keywords: positive-definite solutions
zbMATH Keywords: matrix equation
zbMATH Keywords: solutions of minimal and maximal rank
author: Jürgen Gross
reviewed by: Takayuki Nôno
MaRDI profile type: Publication
cites work: Nonnegative definite and positive definite solutions to the matrix equationAXA*=B
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cites work: Q3153558
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full work available at URL: s0024-3795(00)00033-1
OpenAlex ID: W2145229729
description: scientific article; zbMATH DE number 1563483