Singular value and generalized singular value decompositions and the solution of linear matrix equations
type: Item
instance of: scholarly article
title: Singular value and generalized singular value decompositions and the solution of linear matrix equations
zbMATH Open document ID: 0612.15003
DOI: 10.1016/0024-3795(87)90104-2
author: King-wah Eric Chu
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: All matrices are taken to be real, but not necessarily square. The author employs the singular value decomposition and a generalization of it to study the solvability of the equation \(AXB+CYD=E\), and of the pair of equations \(AXB=E\), \(FXG=H\). A couple of special cases are considered, and numerical algorithms for the solutions are suggested.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 3989558
zbMATH Keywords: linear matrix equations
zbMATH Keywords: generalized inverses
zbMATH Keywords: singular value decomposition
zbMATH Keywords: solvability
reviewed by: George Phillip Barker
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90104-2
OpenAlex ID: W2035780670
cites work: The matrix equation \(AX-YB=C\)
cites work: The matrix equation AXB+CYD=E
cites work: The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
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cites work: Towards a Generalized Singular Value Decomposition
cites work: The Equations AX - YB = C and AX - XB = C in Matrices
cites work: Computing the CS decomposition of a partitioned orthonormal matrix
cites work: The \(\ell_p\)-solution of the linear matrix equation \(AX+YB=C\)
cites work: The Chebyshev solution of the linear matrix equation \(AX+YB=C\)
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description: scientific article; zbMATH DE number 3989558