两个非负定阵的Hadamard积的估计

Estimation of the Hadamard Product ofTwo Nonnegative Definite Matrices

本文以Moore-Penrose逆为工具,讨论满足一定条件的非负定阵A,B的 Hadamard积A·B的估计式,得到了一系列矩阵不等式,推广了已有的结果.我们还证明了A≥0时rk(A·A^+)≥rkA．

:Using Moore-Penrose generalized inverse of a partition matrix,the estimation of A ?B,theHadamard product of two matrices A and B when A≥0, B≥0 ,is discussed under some conditions. A series ofinequalities of matrices is obtained in this note. Some well-known results are expanded. In addition. rk(A·A+)≥rk A is proved.