半正定矩阵广义Schur补的若干不等式

Some Inequalities for generalized Schur Complements of Positive Semi-definite Matrices

利用半正定矩阵的性质和矩阵Moore-Penrose广义逆的特性,研究了半正定矩阵广义Schur补问题.证明了对半正定矩阵A有(A/α)*(A/α)≥A*A/α,并由此得到了一些有关广义Schur补的不等式.将半正定矩阵Schur补的相关结果推广至广义Schur补.

The generalized Schur Complements of positive semi-definite matrices are studied by using the properties of positive semi-definite matrices and their Moore-Penrose generalized inverse. For positive semi-definite matrix A,( A/α)*( A/α)≥A*A/αis proved. Furthermore,some inequalities for generalized Schur com-plements of positive semi-definite matrices are obtained. The relevant results involving Schur complements are extended to the generalized Schur complements.