矩阵和关于广义逆的混合第二吸收律

The Mixed Second Absorption Laws of the Sum of Two Matrices on Generalized Inverse

本文研究了广义逆运算理论,定义了两个矩阵和关于广义逆的混合第一和第二吸收律的概念,利用矩阵的广义Schur补概念与秩方法,对于混合第二吸收律有关的矩阵表达式的极秩进行了研究,推导了这些矩阵表达式的极大秩与极小秩公式,并利用这组公式建立了两个矩阵和关于{1}-逆与{1,3}-逆、{1}-逆与{1,4}-逆的混合第二吸收律成立的充要条件.

In this paper,we investigate the problem of the operation law of the generalized inverse.The concepts of the mixed first and second absorption laws about the generalized inverse are proposed.By using the concept of generalized Schur complement and the matrix rank method,the extremal ranks of matrix expressions which are associated with the mixed second absorption law are investigated,and the formulas of the maximal and minimal ranks of these matrix expressions are derived.Furthermore,the necessary and sufficient conditions of the mixed second absorption laws on{1}-inverse and{1,3}-inverse,{1}-inverse and{1,4}-inverse are established by using these formulas.