Key Words:the least squares mixed-restriction solution; Moore-Penrose generalized inverse; the Kronecker product; the least norm
Abstract:Given A epsilon R-mxn, B epsilon R-nxs, C epsilon R-mxk, D epsilon R-kxs and E epsilon R-mxs, the least squares mixed-restriction solution of matrix equation AXB + CYD = E is studied by using Moore-Penrose generalized inverse and Kronecker product, and its expression is given in this article. Based on this, the expression of the least squares mixed-restriction solution is deprived with the least norm, the necessary and sufficient conditions for the existence of the mixed-restriction solution and its expression are also presented.
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