Abstract
An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimum-norm for the matrix equation A T XB+B T X T A = D. Analytical solution to the matrix equation is also derived. Furthermore, we apply this result to determine the least-squares symmetric and sub-antisymmetric solution of the matrix equation C T XC = D with minimum-norm. Finally, some numerical results are reported to support the theories established in this paper.
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