一矩阵方程组可解条件的研究

J4 ›› 2013, Vol. 48 ›› Issue (10): 47-50.

一矩阵方程组可解条件的研究

江静1,李宁2,王婷1

1.齐鲁师范学院数学系, 山东济南 250013; 2.山东财经大学数学与数量经济学院, 山东济南 250014

收稿日期:2012-12-19 发布日期:2013-10-14
作者简介:江静(1980- ), 女,副教授, 理学博士,研究方向为矩阵方程. Email:jing5099@163.com
基金资助:
国家自然科学基金资助项目(10901093); 齐鲁师范学院青年基金项目(2012L1001)

The solvable condition researched on a pair of matrix equations

JIANG Jing1, LI Ning2, WANG Ting1

1.Department of Mathematics, Qilu Normal University, Jinan 250013, Shandong, China;
2. School of Statistics and Mathematics, Shandong Finance University, Jinan 250014, Shandong, China

Received:2012-12-19 Published:2013-10-14

摘要/Abstract

摘要：

考虑矩阵方程组A1XA*1+B1YB*1=C1
A2XA*2+B2YB*2=C2,其中Ci=C*i,i=1,2。通过矩阵秩的方法得到了该方程组有公共Hermitian解X,Y的一种新的存在性条件,以及方程组有单独的公共Hermitian解X或Y的充分必要条件。

关键词: 矩阵方程组;Hermitian解;最小秩;最大秩

Abstract:

The matrix equations A1XA*1+B1YB*1=C1
A2XA*2+B2YB*2=C2 are studied, where Ci=C*i, i=1, 2. By the rank of matrix, a necessary and sufficient condition is given for the matrix equations to have a pair of common Hermitian solutions X and Y. As a consequence, we have derived the conditions for the matrix equations to have Hermitian solution X or Y respectively by ranks.

Key words: matrix equations; Hermitian solution; minimal rank; maximal rank

中图分类号:

O151

江静1,李宁2,王婷1. 一矩阵方程组可解条件的研究[J]. J4, 2013, 48(10): 47-50.

JIANG Jing1, LI Ning2, WANG Ting1. The solvable condition researched on a pair of matrix equations[J]. J4, 2013, 48(10): 47-50.

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