摘要
Kilmer等提出了一种新的张量乘积t-积,基于该乘积,各种线性代数工具的高维推广已经被验证,其中包括张量奇异值分解、张量特征值定义及有关性质不等式等。基于此对张量的奇异值进行有关分析是有意义的。本文将对Lu等定义的基于t-积的张量奇异值进行扰动分析。首先,给出了张量奇异值的柯西交错定理。然后,将Mirsky提出的关于两个矩阵奇异值差的不等式推广到张量情况下。最后,证明了张量积和张量和的奇异值的一些有用的不等式。
Recently,Kilmer et al.proposed a new tensor product named t-product.Based on this product,various linear algebra tools have been extended from two-dimension to high-dimension,including the singular value decomposition of tensors,eigenvalues of tensors and related properties and inequalities.It is meaningful to analyze the singular values of tensors.In this paper,the perturbation analysis of tensor singular values defined by Lu et al.is studied.Firstly,the Cauchy interlacing theorem for singular values of tensors is given.Then,we extend the Mirsky-type inequality about the singular value difference between two matrices to tensors.Finally,some useful inequalities for the singular values of tensor products and sums of tensors are proved.
作者
张雅婷
解朋朋
Zhang Yating;Xie Pengpeng(School of Mathematical Sciences,Ocean University of China,Qingdao 266100,China)
出处
《中国海洋大学学报（自然科学版）》
CAS
CSCD
北大核心
2023年第S01期120-125,共6页
Periodical of Ocean University of China
基金
国家自然科学基金项目(11801534)资助
关键词
扰动分析
t-积
张量奇异值
柯西交错定理
Mirsky不等式
perturbation analysis
t-product
tensor singular values
Cauchy interlacing theorem
Mirsky inequality
