Relations between least-squares and least-rank solutions of the matrix equation AXB = C

被引：13
作者：
Tian, Yongge [1 ]
Wang, Hongxing [2 ]
机构：
[1] Cent Univ Finance & Econ, CEMA, Beijing, Peoples R China
[2] Huainan Normal Univ, Dept Math, Huainan, Anhui, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 20期
基金：
中国国家自然科学基金;
关键词：
Matrix equation; Least-squares solution; Least-rank solution; Moore-Penrose inverse; Matrix decomposition; Rank formula; MINIMIZATION;
D O I：
10.1016/j.amc.2013.03.137
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A matrix X is called a least-squares solution of the matrix equation AXB = C if it minimizes the F-norm of C - AXB, a least-rank solution of AXB = C if it minimizes the rank of C - AXB. These two types of solution are not necessarily the same. In this paper, we establish necessary and sufficient conditions for the two types of solutions to coincide by using some matrix rank formulas and nested decompositions of matrices. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：10293 / 10301
页数：9
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