Tensor Transpose and Its Properties
arXiv:1411.1503
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It provides a theoretical foundation for tensor transpose, which is of interest to researchers in multilinear algebra and tensor computations.
This paper defines tensor transpose using permutations and symmetry groups, and studies its properties including classification, composition, and relationships with tensor multiplication, eigenvalues, decompositions, and rank.
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.