The reflexive and anti-reflexive solutions of the matrix equation AX=B

The Least Squares Hermitian (Anti)reflexive Solution with the Least Norm to Matrix Equation AXB=C

“…Then the least squares Hermitian reflexive solution is given by (18). Obviously, the least squares Hermitian reflexive solution with the least norm is given by (20).…”

The generalized centro-symmetric and least squares generalized centro-symmetric solutions of the matrix equation AYB + CYTD = E

“…In [48], the necessary and sufficient conditions for the solvability of matrix equation A H XB = C (including the matrix Equation (43) as a special case) over the generalized centro-symmetric matrix X were given, and the general expression of the solution for a solvable case was obtained. The method [48] needs to compute the following decompositions for A , B and symmetric orthogonal matrix P: …”

The Structure of Symmetric Solutions of the Matrix Equation AX=B over a Principal Ideal Domain

“…They are given necessary and sufficient conditions (using generalized inverses) for the existence of symmetric ( [7][8][9][10]), symmetric with prescribed rank [11], Hermitian and skew-Hermitian ( [12,13]), reflexive and antireflexive [14], and general solutions which are described in terms of original elements or operators. Methods for constructed symmetric solutions of linear matrix equation = are proposed in [9,13,15,16].…”