Abstract
An n × n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2 = I . An n × n complex matrix A is said to be a ( P , Q ) generalized reflexive (or anti-reflexive) matrix with respect to the generalized reflection matrix dual ( P , Q ) if A = PAQ (or A = - PAQ ). This paper establishes the necessary and sufficient conditions for the existence of and the expressions for the ( P , Q ) generalized reflexive and anti-reflexive solutions of the matrix equation AX = B . In addition, in corresponding solution set of the equation, the explicit expression of the nearest matrix to a given matrix in the Frobenius norm has been provided.
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