Singular value and generalized singular value decompositions and the solution of linear matrix equations. (English) Zbl 0612.15003

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.
Reviewer: G.P.Barker


15A18 Eigenvalues, singular values, and eigenvectors
15A24 Matrix equations and identities
15A09 Theory of matrix inversion and generalized inverses
Full Text: DOI


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