The moore-penrose inverse of a free matrix

被引：0

作者：

Britz, Thomas ^{[1
]}

机构：

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2007年 / 16卷

关键词：

free matrix; moore-penrose inverse; bipartite graph; directed graph;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A matrix is free, or generic, if its nonzero entries are algebraically independent. Necessary and sufficient combinatorial conditions are presented for a complex free matrix to have a free Moore-Penrose inverse. These conditions extend previously known results for square, nonsingular free matrices. The result used to prove this characterization relates the combinatorial structure of a free matrix to that of its Moore-Penrose inverse. Also, it is proved that the bipartite graph or, equivalently, the zero pattern of a free matrix uniquely determines that of its Moore-Penrose inverse, and this mapping is described explicitly. Finally, it is proved that a free matrix contains at most as many nonzero entries as does its Moore-Penrose inverse.

引用

页码：208 / 215

页数：8

共 50 条

[1] The Moore-Penrose inverse of a companion matrix
Patricio, Pedro
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (03) : 870 - 877
[2] MOORE-PENROSE INVERSE OF A SYMMETRICAL MATRIX
ABDULLAH, J
NEUDECKER, H
SHUANGZHE, L
[J]. ECONOMETRIC THEORY, 1993, 9 (04) : 703 - 703
[3] On the Moore-Penrose generalized inverse matrix
Rakha, MA
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 158 (01) : 185 - 200
[4] THE MOORE-PENROSE INVERSE OF A SYMMETRICAL MATRIX
TRENKLER, G
MAGNUS, JR
[J]. ECONOMETRIC THEORY, 1992, 8 (04) : 585 - 586
[5] On the perturbation of the Moore-Penrose inverse of a matrix
Xu, Xuefeng
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2020, 374 (374)
[6] Perturbations of Moore-Penrose inverse and dual Moore-Penrose generalized inverse
Cui, Chong
Wang, Hongxing
Wei, Yimin
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2023, 69 (06) : 4163 - 4186
[7] Perturbations of Moore-Penrose inverse and dual Moore-Penrose generalized inverse
Chong Cui
Hongxing Wang
Yimin Wei
[J]. Journal of Applied Mathematics and Computing, 2023, 69 : 4163 - 4186
[8] The density of the Moore-Penrose inverse of a random matrix
Neudecker, H
Liu, SZ
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1996, 237 : 123 - 126
[9] Weighted Moore-Penrose inverse of a Boolean matrix
Bapat, RB
Jain, SK
Pati, S
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 255 : 267 - 279
[10] The property of Moore-Penrose generalized inverse matrix
Tian Baoguang
Wang Nannan
Xia Lei
[J]. PROCEEDINGS OF THE THIRD INTERNATIONAL WORKSHOP ON MATRIX ANALYSIS AND APPLICATIONS, VOL 2, 2009, : 289 - 292

← 1 2 3 4 5 →