关于矩阵函数方程f(X)=A的解

华东师范大学学报(自然科学版) ›› 2005, Vol. 2005 ›› Issue (1): 28-33.

关于矩阵函数方程f(X)=A的解

程学翰¹, 刘爱晶^1,2

1. 华东师范大学数学系, 上海 200062 2.曲阜师范大学数学系, 山东曲阜 273165

收稿日期:2003-01-03 修回日期:2003-03-17 出版日期:2005-03-25 发布日期:2005-03-25
通讯作者: 程学翰

The Solutions of Matrix Function Equation f(X)=A(Chinese)

CHENG Xue-han¹ , LIU Ai-jing ^{1, 2}

1. Department of mathematics, East China Normal University, Shanghai 200062, China; 2. Department of mathematics , Qufu Normal University, Shandong 273165, China

Received:2003-01-03 Revised:2003-03-17 Online:2005-03-25 Published:2005-03-25
Contact: CHENG Xue-han

摘要/Abstract

摘要： 给出了复数域上矩阵函数方程f(X)=A有解的充要条件, 其中 A∈C ^n×n ,f(x) 为复值函数.进一步给出可以用A的多项式来表示方程的解的充要条件.

关键词: 矩阵方程, 矩阵函数, 矩阵函数方程的解, 矩阵方程, 矩阵函数, 矩阵函数方程的解

Abstract: We give the sufficient and necessary conditions of the solutions for matrix function equations f(X)=A , where A∈^Cn×n .We study the expression of the solutions by the polynomial of A, also give the sufficient and necessary conditions.

Key words: matrix function, solutions of matrix function equations, matrix equation, matrix function, solutions of matrix function equations

中图分类号:

O151.2

程学翰;刘爱晶;. 关于矩阵函数方程f(X)=A的解[J]. 华东师范大学学报(自然科学版), 2005, 2005(1): 28-33.

CHENG Xue-han;LIU Ai-jing;. The Solutions of Matrix Function Equation f(X)=A(Chinese)[J]. Journal of East China Normal University(Natural Sc, 2005, 2005(1): 28-33.