On the tensor Permutation Matrices

TL;DR

This paper explores tensor permutation matrices, demonstrating their ability to permute tensor products of rectangular matrices and providing examples related to tensor commutation matrices for solving linear matrix equations.

Contribution

It introduces the concept of tensor permutation matrices and illustrates their application in permutating tensor products and solving matrix equations.

Findings

Tensor permutation matrices can permute tensor products of rectangular matrices.

Examples of tensor commutation matrices are provided for linear matrix equations.

The paper offers insights into the structure and applications of tensor permutation matrices.

Abstract

We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.