The Solvability Conditions for the Positive Semi-Definite Solution and Positive Definite Solution of the Linear Matrix Equation (A~TXA, B~TXB) = (C, D)

摘要

In [3], Chang and Wang have discussed the symmetric solutions of the linear matrix equation (A~TXA, B~TXB) - (C,D). In this paper, we obtain the conditions for the existence of and the general expressions for the symmetric positive semi-definite solution and symmetric positive definite solution of this equation by applying the quotient singular value decomposition (QSVD) of a matrix pair.