Abstract
ABSTRACTIn this paper, we establish some conditions for the existence and the representations for the Hermitian reflexive and Hermitian anti-reflexive, and non-negative definite reflexive solutions to the matrix equation AX=B with respect to a generalized reflection matrix P by using the Moore–Penrose inverse. Moreover, in corresponding solution sets of the equation, the explicit expressions of the nearest matrix to a given matrix in the Frobenius norm have been provided.
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