摘要
1.引言 令Rn×m表示所有n×m实矩阵集合,Cn×m表示所有n×m复矩阵集合,Cn=Cn×1,HCn×n表示所有n阶Hermite矩阵集合,UCn×n表示所有n阶酉矩阵集合,AHCn×n表示所有n阶反Hermite矩阵集合,R(A)表示A的列空间,N(A)表示A的零空间,A+表示A的Moore—Penrose广义逆,A*B表示A与B的Hadamard积,rank(A)表示矩阵A的秩.tr(A)表示矩阵A的迹.矩阵A,B的内积定义为(A,B)=tr(BHA),A,B∈Cn×m,由此内积诱导的范数为||A||=√(A,A)=[tr(AHA)]1/2,则此范数为Frobenius范数,并且Cn×m构成一个完备的内积空间,In表示n阶单位阵,i=√-1,记OASRn×n表示n×n阶正交反对称矩阵的全体。
Let OASR =
Given J OASR,A C is termed generalized Hamilton matrix if JAT = AH. we denote the set of all n x n generalized Hamilton matrics by HTC, AC is termed generalized antihamilton matrix if JAJ = -AH. We denote the set of all n x n generalized antihamilton matrices by AHTC.
A 6 C is termed Hermite-generalized antihamilton matrix if
AH = A and JAJ = -AH. We denote the set of all n x n Hermite-generalized antihamilton matrices by
Let Where U = (U1, U2) UC,
In this paper, we discuss the following two problems: Problem I. Given X,B C, Find A S such that
Problem II. Given A* C, Find A SE such that
Where is Frobenius norm, and SE is the solution set of Problem I.
The general representation of SE has been given. The necessary and sufficient conditions have been presented for f(A) = 0. For Problem II the expression of the solution has been provided.
出处
《计算数学》
CSCD
北大核心
2003年第2期209-218,共10页
Mathematica Numerica Sinica
基金
国家自然科学基金资助项目(10171031).