Li Yao-Tang, Li Zheng-Bo, Liu Qi-Long, Liu Qiong
School of Mathematics and Statistics, Yunnan University, Kunming, 650091 People's Republic of China.
Springerplus. 2016 Nov 28;5(1):2023. doi: 10.1186/s40064-016-3720-1. eCollection 2016.
The permutation transformation of tensors is introduced and its basic properties are discussed. The invariance under permutation transformations is studied for some important structure tensors such as symmetric tensors, positive definite (positive semidefinite) tensors, -tensors, -tensors, Hankel tensors, -tensors, -tensors and -tensors. Finally, as an application of permutation transformations of tensors, the canonical form theorem of tensors is given. The theorem shows that some problems of higher dimension tensors can be translated into the corresponding problems of lower dimension weakly irreducible tensors so as to handle easily.
介绍了张量的置换变换，并讨论了其基本性质。研究了一些重要结构张量（如对称张量、正定（半正定）张量、 -张量、 -张量、汉克尔张量、 -张量、 -张量和 -张量）在置换变换下的不变性。最后，作为张量置换变换的一个应用，给出了张量的标准型定理。该定理表明，一些高维张量问题可以转化为低维弱不可约张量的相应问题，从而便于处理。
