## Abstract

Given two linear transformations, with representing matrices A and B with respect to some bases, it is not clear, in general, whether the Tracy-Singh product of the matrices A and B corresponds to a particular operation on the linear transformations. Nevertheless, it is not hard to show that in the particular case that each matrix is a square matrix of order of the form n^{2}, n > 1, and is partitioned into n^{2} square blocks of order n, then their Tracy-Singh product, (Formula presented.), is similar to (Formula presented.), and the change of basis matrix is a permutation matrix. In this note, we prove that in the special case of linear operators induced from set-theoretic solutions of the Yang-Baxter equation, the Tracy-Singh product of their representing matrices is the representing matrix of the linear operator obtained from the direct product of the set-theoretic solutions.

Original language | English |
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Journal | Communications in Algebra |

DOIs | |

State | Accepted/In press - 2024 |

### Bibliographical note

Publisher Copyright:© 2024 Taylor & Francis Group, LLC.

## Keywords

- Representing matrices of linear operators
- Tracy-Singh product of matrices
- set-theoretic solutions of the Yang-Baxter equation
- the Yang-Baxter equation

## ASJC Scopus subject areas

- Algebra and Number Theory