نبذة مختصرة : In this paper, the linear matrix equation X = AXB * + BXA * + Q is considered, which is called the mixed-type Lyapunov equation. Some necessary and sufficient conditions for the existence of a unique solution are presented. Since a Hermitian positive semidefinite solution is important from the application point of view, some sufficient conditions for the existence of a Hermitian positive semidefinite solution are derived.
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