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On solutions of matrix equation \(AXB+CYD=F\). (English) Zbl 0933.15024

Summary: The matrix equation with two unknown matrices \(X,Y\) of the form \(AXB+CYD=F\) is discussed. By applying the canonical correlation decomposition of matrix pairs, we obtain expressions of the least-squares solutions of the matrix equation, and sufficient and necessary conditions for the existence and uniqueness of the solutions. We also derive a general form of the solutions. We also study the least-squares Hermitian (skew-Hermitian) solutions of equation \(AXA^H+CYC^H=F\).

MSC:

15A24 Matrix equations and identities
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