On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices

Year 2025, Volume: 14 Issue: 3, 237 - 256, 31.12.2025

Efruz Özlem Mersin , Mustafa Bahşi

https://doi.org/10.54187/jnrs.1705030

Abstract

In this study, we focus on the commutators and anti-commutators of the matrix
exponential, trigonometric, and hyperbolic functions of the nth order exchange matrix Ψ
with an arbitrary matrix Λ. We also explore their behaviour under recursive commutator
and anti-commutator operations to highlight structural patterns and interactions between
such matrices. Moreover, we emphasize the connection of these results with Sylvester matrix
equations, which provides both theoretical insights and potential applications.

Keywords

Anti-commutators , commutators , matrix functions , Sylvester matrix equation

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