![]() Finally, we draw some conclusions in the last section. In fifth section, we will give the canonical form theorem of tensors and a numerical example which shows that some problems of higher dimension tensors can be translated into the corresponding problems of lower dimension weakly irreducible tensors by using permutation transformations. In fourth section, we will discuss the invariance under permutation transformations for some important structure tensors such as symmetric tensors, positive definite tensors, M-tensors, Hankel tensors, P-tensors, B-tensors, H-tensors and so on. In third section, we will discuss basic properties of permutation transformations of tensors. In the next section, we will introduce the permutation transformation of tensors and give its expression. Inspired by this, we introduce permutation transformations of tensors, and discuss its basic properties and and their applications in this paper. tensor permuteindices Permutation of the indices of a tensortype Calling Sequence Parameters Description Examples Calling Sequence permuteindices( T, permutation ) Parameters T - tensortype on which to perform permutation permutation - permutation. Some problems of higher dimension reducible matrices can be translated into the corresponding problems of lower dimension irreducible matrices by using the permutation transformation of matrices. Constructor TensorMap(data, size0, size1.Therefore, it is interesting that how to translate problems of higher dimension reducible tensors into the corresponding problems of lower dimension irreducible tensors.Īs we all know, the permutation transformation of matrices plays a very important role in linear algebra and matrix theory. A TensorMap is not resizable because it does not own the memory where its data are stored. We can also permute a tensor with new dimension using Tensor.permute(). For example, a tensor with dimension 2, 3 can be permuted to 3, 2. It doesn't make a copy of the original tensor. It returns a view of the input tensor with its dimension permuted. In the researches on tensors with its application, the reducibility and higher dimension of tensors are two important factors to cause difficulties. torch.permute() method is used to perform a permute operation on a PyTorch tensor. permute(self, order) By applying this function it will return the sptensor object that is permuted by. Lately, the research topic on structure tensors has also attracted much attention, such as symmetric tensors (Qi 2005), \(P(P_0)\)-tensors (Song and Qi 2014), \(B(B_0)\)-tensors (Song and Qi 2014), Z-tensors (Zhang et al. ndarray object that has the same values with the sptensor. The study of tensors with their various applications has attracted extensive attention and interest, since the work of Qi ( 2005) and Lim ( 2005).
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