厦门大学学报（自然科学版）2012，Vol.51Issue(1)：9-11,3.
张量与张量转置的特征值问题
The Eigenvalue Problems for Tensor and Tensor Transposition
摘要
Abstract
The tensor eigenproblem has many important applications. This paper studies the eigenproblem for tensor and tensor transposition,and proves that the mode-p, eigenpair of tensor is the same as the mode-I eigenpair of p-transposition of tensor. It is illustrated by examples that the mode-z eigenvalue of tensor is not necessarily equal to that of p-transposition of tensor,and the eigenvectors corresponding to the mode-I eigenvalueμ, and the mode-j eigenvalue μ, are not orthogonal when μ,≠μ Therefore,the results show that the properties of eigenvalues of matrix can not be completely extended to tensor. Based on this conclusion, this paper gives a condition that the index vector p should satisfy when the mode-z eigenpair of tensor is equal to that of the p-transposition of tensor.关键词
张量/张量转置/特征值/特征向量/正交Key words
tensors tensor transposition/eigenvalue/eigenvector/orthogonality分类
数理科学引用本文复制引用
陈震,卢琳璋,刘智秉..张量与张量转置的特征值问题[J].厦门大学学报（自然科学版）,2012,51(1):9-11,3.基金项目
国家自然科学基金项目(10961010) （10961010）
贵州省科学技术基金项目(黔科合J字LKS[2009]03号) （黔科合J字LKS[2009]03号）
