三模Tucker积张量秩的一些性质  

Some properties of the tensor rank under 3-mode Tucker product

作　　者：张双 韩乐[1] ZHANG Shuang;HAN Le(School of Mathematics,South China University of Technology,Guangzhou 510640,China)

机构地区：[1]华南理工大学数学学院,广东广州510640

出　　处：《高师理科学刊》2020年第11期14-18,共5页Journal of Science of Teachers＇College and University

基　　金：教育部人文社科青年基金资助项目(17YJC630026);华南理工大学研究生全英文课程建设项目(Y2181421)。

摘　　要：张量Tubal秩的定义不止一种,但本质上是用离散傅立叶变换矩阵对原始张量做三模Tucker积得到一个复张量,这个复张量所有前片秩的最大值就是张量Tubal秩.借助三模Tucker积从代数角度研究三阶张量Tubal秩的计算,并给出原始张量与变换后的复张量之间CP秩、Tucker秩的关系.Although there are some definitions of the Tubal rank,in essence,the Tubal rank of tensor is the maximum of the ranks of the frontal slices of a complex tensor,that is obtained by the 3-mode Tucker product with the discrete Fourier Transformation.The calculation of the Tubal rank of the third-order tensors is researched from the algebraic perspective by means of the 3-mode Tucker product,and the relationships of CP rank and Tucker rank between the original tensor and the complex tensor was given.

关 键 词：Tucker积 Tubal秩 CP秩 Tucker秩 

分 类 号：O151[理学—数学]