Least-squares solutions and least-rank solutions of the matrix equation AXA* = B and their relations

被引：7

作者：

Tian, Yongge ^{[1
]}

机构：

[1] Cent Univ Finance & Econ, CEMA, Beijing 100081, Peoples R China

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 2013年 / 20卷 / 05期

关键词：

matrix equation; least-squares solution; least-rank solution; Moore-Penrose inverse; SVD; rank formula; POSITIVE-DEFINITE SOLUTIONS; NONNEGATIVE-DEFINITE; EXTREMAL RANKS; MINIMIZATION; EXPRESSIONS;

D O I：

10.1002/nla.829

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Hermitian matrix X is called a least-squares solution of the inconsistent matrix equation AXA* = B, where B is Hermitian. A* denotes the conjugate transpose of A if it minimizes the F-norm of B - AXA*; it is called a least-rank solution of AXA* = B if it minimizes the rank of B - AXA*. In this paper, we study these two types of solutions by using generalized inverses of matrices and some matrix decompositions. In particular, we derive necessary and sufficient conditions for the two types of solutions to coincide. Copyright (C) 2012 John Wiley & Sons, Ltd.

引用

页码：713 / 722

页数：10

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