摘要
借助矩阵张量积和矩阵数值半径的性质,证明了不等式r(A_(1)…A_(k))≥k_(i)=1r(A_(i))和等式r(A■B)=r(B■A),其中A_(1),…,Ak,A,B∈L(U).同时,举例说明了不等式r(k■A)≤r^(k)(A)不成立,而当A_(1),…,A_(k)为正规阵时,有r(A_(1)■…■A_(k))=ks=1r(A_(s)).
This paper proves that for any n×n matrices A_(1),...,A_(k)∈L(U)we have r(A_(1)...A_(k))≥ki=1r(A_(i));and for any two n×n matrices A,B∈L(U)we have r(A■B)=r(B■A);where r(A)denotes the numerical radius of A.And it shows that the inequalities r(A■B)≤r(A)r(B)and r(A■A)≤r2(A)do not hold in general,particularly,r(A_(1)■...■A_(k))=ks=1r(A_(S))for normal matrices A_(1),A_(2),...,A_(k).
作者
刘修生
LIU Xiu-sheng(Department of Fundamental Courses,Huangshi College,Huangshi,Hubei 435003;College of Mathematics and Statistics,Wuhan University,Wuhan 430072)
出处
《华中师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2003年第1期14-16,共3页
Journal of Central China Normal University:Natural Sciences
基金
国家重点基础研究发展规划资助项目
湖北省教育厅重大项目资助(2001Z06003).
关键词
矩阵的数值半径
矩阵和向量的张量积
向量内积
矩阵和向量范数
numerical radius of matrix
tensor product of matrix and vector
inner product
operator norm of matrix and vector
作者简介
刘修生(196O-),男,湖北大治人,副教授.主要从事代数与数论研究.
