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The symmetric ortho-symmetric maximal and minimal rank solutions to a class of matrix equation and their optimal approximation are considered. By applying the matrix rank method, the necessary and sufficient conditions for the existence of the maximal and minimal rank solutions with symmetric ortho-symmetric to the equation. The expressions of such solutions to this equation are also given when the...
Applying the generalized singular value decomposition (GSVD) of matrices, the set of the centro-symmetric matrix solution with prescribed ranks to the matrix equation B AX = is presented. The expression of the optimal approximation solution to the set of the minimal rank solution m S is provided.
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