A Hermitian least squares solution of the matrix equation AXB=C A X B = C subject to inequality restrictions ?
This paper gives some closed-form formulas for computing the maximal and minimal ranks and inertias of P?X P ? X with respect to X X , where P ? C H n is given, and X X is a Hermitian least squares solution to the matrix equation AXB=C A X B = C . We derive, as applications, necessary and sufficient conditions for X ? ( ? , > , < ) P in the Lwner partial ordering. In addition, we give necessary and sufficient conditions for the existence of a Hermitian positive (negative, nonpositive, nonnegative) definite least squares solution to AXB=C A X B = C .
least squares solution matrix equation rank inertia hermitian solution generalized inverse