半正定矩阵Kronecker积的伪Schur补的几点注记

Some results on generalized Schur complements for the Kronecker product of positive semidefinite matrices

摘要: 利用矩阵Kronecker积和置换矩阵的相关性质研究了半正定矩阵Kronecker积的伪Schur补问题,得到了关于半正定矩阵Kronecker积的伪Schur补的一个等式,将其结果推广至半正定矩阵的伪Schur补上,并适当改变γ'的构成得出有关半正定矩阵Kronecker积的伪Schur补的一些不等式.

Abstract: The generalized Schur complements for the Kronecker product of positive semidefinite matrices are studied with the properties of the Kronecker product and the permutation matrix.An identity of generalized Schur complements for the Kronecker product of positive semidefinite matrices is obtained,which extend the result to the generalized Schur complements of positive semidefinite matrices.Further,some inequalities are derived by properly changing the composition of γ'.