On the symmetric solutions of linear matrix equations. (English) Zbl 0712.15009
Necessary and sufficient conditions are given for the existence of symmetric solutions of the matrix equations \(AX=C\) and \(AXB=C\) on the real field, in terms of the singular value decomposition of A and the generalized singular value decomposition of the pair \((A,B^ T)\), respectively. Expressions for the general solution are provided for each case.
Reviewer: M.E.Sezer
References:
| [1] | Vetter, W. J., Vector structures and solutions of linear matrix equation, Linear Algebra Appl., 10, 181-188 (1975) · Zbl 0307.15003 |
| [2] | Magnus, J. R.; Neudecker, H., The elimination matrix: Some lemmas and applications, SIAM J. Algebraic Discrete Methods, 1, 422-429 (1980) · Zbl 0497.15014 |
| [3] | Henk Don, F. J., On the symmetric solutions of a linear matrix equation, Linear Algebra Appl., 93, 1-7 (1987) · Zbl 0622.15001 |
| [4] | Golub, G. H.; Van Loan, C. F., Matrix Computations (1983), Johns Hopkins U.P: Johns Hopkins U.P Baltimore · Zbl 0559.65011 |
| [5] | Paige, C. C.; Saunders, M. A., Towards a generalized singular value decomposition, SIAM J. Numer. Anal., 18, 398-405 (1981) · Zbl 0471.65018 |
| [6] | Stewart, G. W., Computing the CS-decomposition of a partitioned orthogonal matrix, Numer. Math., 40, 297-306 (1982) · Zbl 0516.65016 |
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