Separable Symmetric Tensors and Separable Anti-symmetric Tensors  

作　　者：Changqing Xu Kaijie Xu 

机构地区：[1]School of Mathematical Sciences,Suzhou University of Science and Technology,Suzhou,215009,Jiangsu,China [2]School of Electronic Engineering,Xidian University,Xi’an,710071,Shaanxi,China

出　　处：《Communications on Applied Mathematics and Computation》2023年第4期1509-1523,共15页应用数学与计算数学学报（英文）

摘　　要：In this paper,we first initialize the S-product of tensors to unify the outer product,contractive product,and the inner product of tensors.Then,we introduce the separable symmetry tensors and separable anti-symmetry tensors,which are defined,respectively,as the sum and the algebraic sum of rank-one tensors generated by the tensor product of some vectors.We offer a class of tensors to achieve the upper bound for rank(A)≤6 for all tensors of size 3×3×3.We also show that each 3×3×3 anti-symmetric tensor is separable.

关 键 词：S-product Invertible tensor Separable symmetric tensor Separable anti-symmetric tensor 

分 类 号：O17[理学—数学]