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\( (P,Q)\) generalized reflexive solution and inverse reflexive solution of matrix equation \({A^H}XB = C\). (Chinese. English summary) Zbl 1438.15036

Summary: The necessary and sufficient conditions for the existence and the expressions for \( (P,Q)\) generalized reflexive and anti-reflexive solutions of the matrix equation \({A^H}XB = C\) are given. Moreover, the relative optimal approximation problem is considered. The explicit expressions of the optimal approximation solution and the minimum norm solution are both provided.

MSC:

15A24 Matrix equations and identities
65F45 Numerical methods for matrix equations
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