长方矩阵加权群逆的计算

Calculation of Weighted Group Inverse of Rectangular Matrix

矩阵的广义逆的概念是由美国学者E.H.Moore首先提出的。1920年,他用投影矩阵定义了矩阵唯一的广义逆。广义逆在微分方程、数值代数、线性统计推断、最优化、电网络分析等问题中起着非常重要的作用。2007年,岑建苗教授在文中首次引入了长方矩阵的加权群逆的概念。加权群逆不同于Cline与Greville提出的长方矩阵的加权Drazin逆的概念。因此,对它的研究是有意义且很有必要的。本文主要研究长方矩阵加权群逆的计算。利用矩阵的1-逆和群逆,从加权群逆的不同表示方法中给出加权群逆的计算。

The concept of generalized inverse of matrix was first proposed by American scholar E.H.Ore.In 1920,he defined the unique generalized inverse of a matrix by a projection matrix.Generalized inverse plays an important role in differential equations,numerical algebra,linear statistical inference,optimization,and electrical network analysis.In 2007,Professor Cen Jianmiao first introduced the concept of weighted group inverse of rectangular matrix in his paper The weighted group inverse is different from the weighted Drazin inverse of the rectangular matrix proposed by Cline and Greville.Therefore,it is meaningful and necessary to study it.This paper mainly studies the calculation of weighted group inverse of rectangular matrix.By using 1-inverse and group inverse of matrix,the calculation of weighted group inverse is given from different representation methods of weighted group inverse.