矩阵的泛正定与广义逆偏序

UNIVERSAL POSITIVE DEFINITENESS AND THE PARTIAL ORDERING OF GENERALIZED INVERSES OF A MATRIX

引言出现在二次型和 Hermite 型研究中的正定矩阵不仅理论结果非常丰富,而且在几乎所有的数值分析以及应用数学和力学各分支中有着广泛的应用.我们用 P_n 表示所有 n

In order to study the problem of partial ordering of generalized inverse matrices,the uni-versal positive definite matrix is introduced in this paper.Some problems in discussing this kind of partial ordering in the existing literature arepointed out,and some sufficient,necessary and sufficient conditions for existence of the par-tial ordering between generalized inverse matrices under new definitions of the partial orderingare given.