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Tensor Permutation Matrices in Finite Dimensions

Rakotonirina Christian
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Abstract

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation matrix. Some tensor commutation matrix has been expressed by using the Gell-Mann matrices.

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Rakotonirina Christian. 2005-10-28. Tensor Permutation Matrices in Finite Dimensions. https://arxiv.org/abs/math/0508053

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