Upper and lower bounds for the rank of the matrix-valued function A plus BXC when X has a fixed rank

被引：1

作者：

Tian, Yongge ^{[1
]}

机构：

[1] Cent Univ Finance & Econ, China Econ & Management Acad, Beijing, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2017年 / 65卷 / 10期

关键词：

Matrix-valued function; rank; matrix decomposition; partially-specified matrices; 15A23; 15A24; 65F05; SINGULAR-VALUE DECOMPOSITION; APPROXIMATION; TRIPLETS;

D O I：

10.1080/03081087.2017.1322034

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a matrix-valued function f(X) = A + BXC, where A. Cmxn, B. Cmxp, and C. Cqxn are known matrices, we first review two known fundamental formulas for calculating the maximum and minimum ranks of the matrix-valued function f(X) when X runs over Cpxq. We then establish some new formulas for calculating the maximum and minimum ranks of f(X) when X runs over Cpxq with a restriction rank(X) = t by using a simultaneous decomposition of A, B and C, and some tricky matrix operations. Some applications of the rank formulas in completing partially-specified matrices are also given.

引用

页码：2101 / 2113

页数：13