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


15A24 Matrix equations and identities
15A18 Eigenvalues, singular values, and eigenvectors
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