GENERALIZED INVERSES OVER INTEGRAL-DOMAINS

被引：48

作者：

BAPAT, RB ^{[1
]}

RAO, KPSB ^{[1
]}

PRASAD, KM ^{[1
]}

机构：

[1] INDIAN STAT INST,BANGALORE 560059,INDIA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1990年 / 140卷

关键词：

D O I：

10.1016/0024-3795(90)90229-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In an earlier paper one of the authors showed that a matrix of rank r over an integral domain has a generalized inverse if and only if a linear combination of all the r × r minors of the matrix is one. In the same paper a procedure for constructing a generalized inverse from such a linear combination was also given. In the present paper we show that any reflexive generalized inverse can be obtained by that procedure. We also show that if the integral domain is a principal ideal domain, every generalized inverse can be obtained by that procedure. It is also shown that a matrix A of rank r over an integral domain has Moore-Penrose inverse if and only if the sum of squares of all r × r minors of A is an invertible element of the integral domain. © 1990.

引用

页码：181 / 196

页数：16