摘要
对于任意奇异的Hermitian矩阵A,存在一个非平凡k次单位矩阵R使得A为k次R-对称矩阵。给定k次单位矩阵R,给出了k次R-对称矩阵的特征对的性质、特征多项式的计算公式和奇异值分解,并利用此类广义对称矩阵的特殊结构将其特征问题降阶,转化成若干个低价矩阵的特征问题来计算。
For every singular Hermitian matrix A, there exists a k-th unit matrix R such that A is k degree R-symmetric. Sup- pose that a k- th unit matrix R is given for a k degree R-symmetric matrix A. It presents the properties of its eigen-pairs, the ex- plicit expression of its characteristic polynomial, and its singular value decomposition. Moreover, an eigen-problem of A can be reduced to multi eigen-problems of matrices of small dimensions by applying its structure.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2007年第12期15-18,共4页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(10771013)
山东省自然科学基金资助项目(Y2005A12)
关键词
广义对称矩阵
特征对
特征多项式
奇异值分解
generalized symmetric matrix
eigen-pair
characteristic polynomial
singular value decomposition
