The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive de...The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.展开更多
In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.
文摘The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.
文摘In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.
