title: Permutation transformations of tensors with an application.
abstract: 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,Z-tensors,M-tensors, Hankel tensors,P-tensors,B-tensors andH-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.
authors.affiliation: School of Mathematics and Statistics, Yunnan University, Kunming, 650091 People's Republic of China.
authors.forename: Yao-Tang
authors.initials: YT
authors.lastname: Li
authors.affiliation: School of Mathematics and Statistics, Yunnan University, Kunming, 650091 People's Republic of China.
authors.forename: Zheng-Bo
authors.initials: ZB
authors.lastname: Li
authors.affiliation: School of Mathematics and Statistics, Yunnan University, Kunming, 650091 People's Republic of China.
authors.forename: Qi-Long
authors.initials: QL
authors.lastname: Liu
authors.affiliation: School of Mathematics and Statistics, Yunnan University, Kunming, 650091 People's Republic of China.
authors.forename: Qiong
authors.initials: Q
authors.lastname: Liu
keywords: Canonical form; Permutation transformation; Structure tensor; Weakly irreducible tensor