科研之友
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摘要
This paper gives some closed-form formulas for computing the maximal and minimal ranks and inertias of P - X with respect to X, where P is an element of C-H(n) is given, and X is a Hermitian least squares solution to the matrix equation AXB = C. We derive, as applications, necessary and sufficient conditions for X >= (<=, >, <)P in the Lowner 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.
