Sums of rank-one matrices and ranks of principal submatrices

被引：1

作者：

Fallat, Shaun M. ^{[1
]}

Tifenbach, Ryan M. ^{[2
]}

机构：

[1] Univ Regina, Dept Math & Stat, Regina, SK, Canada

[2] Saskatchewan Polytech, Sch Arts & Sci, Moose Jaw, SK, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2021年 / 69卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Symmetric matrices; Hermitian matrices; principal submatrix; matrix rank; principal rank property; matrix positivity; principal rank;

D O I：

10.1080/03081087.2017.1406446

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present three new results, each concerned with ranks of principal submatrices. The first connects the ranks of sums of rank-one matrices with that of certain associated partial sums. The other results concentrate on the ranks of certain submatrices of given matrix products. In addition, two related applications are provided, with one involving full-rank principal submatrices, while the other is concerned with matrix positivity.

引用

页码：9 / 18

页数：10

共 6 条

[1]

Fallat S.M., 2011, Princeton Series in Applied Mathematics

[2] Bidiagonal factorizations of totally nonnegative matrices [J].