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

作　　者：李莹[1,2] 高岩[1] 郭文彬[2] 司成海[2] LI Ying;GAO Yan;GUO Wen-bin;SI Cheng-hai(School of Management,University of Shanghai for Science and Technology,Shanghai 200093;College of Mathematical Science,Liaocheng University,Liaocheng,Shandong 252059)

机构地区：[1]上海理工大学管理学院,上海200093 [2]聊城大学数学科学学院,山东聊城252059

出　　处：《工程数学学报》2011年第4期519-526,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10771073);山东省自然科学基金(ZR2009AL006)

摘　　要：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.

关 键 词：M-P逆 {i j k}-逆 广义SCHUR补 秩方法 混合吸收律 

分 类 号：O151.21[理学—数学]