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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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##### References:
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