Solvability of a quaternion matrix equation
The author studies the solvability of the matrix equations \((*)\) \(AXB=D\) and \((**)\) \(A^*X^*B^*\pm BXA=D\) where \(A\), \(B\), \(D\) are quaternion matrices. He gives necessary and sufficient conditions for the solvability of \((*)\) (resp. of \((**)\)) in Hermitian and in skew-Hermitian matrices (resp. in quaternion matrices), and he presents formulas for the general solutions when the conditions are met. These formulas involve the matrices \(A\), \(B\), \(D\) and their Moore-Penrose inverses. (The Moore-Penrose inverse \(A^+\) of the \(m\times n\) quaternion matrix \(A\) is an \(n\times m\)-matrix \(X\) satisfying the conditions \(AXA=A\), \(XAX=X\), \((AX)^*=AX\), \((XA)^*=XA\).).
scientific article; zbMATH DE number 1877156