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

Efruz Özlem Mersin; Mustafa Bahşi

doi:10.54187/jnrs.1705030

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

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

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Efruz Özlem Mersin ^*
0000-0001-6260-9063
Türkiye

Mustafa Bahşi
0000-0002-6356-6592
Türkiye

Publication Date

December 31, 2025

Submission Date

May 23, 2025

Acceptance Date

October 3, 2025

Published in Issue

Year 2025 Volume: 14 Number: 3

DOI

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

IZ

https://izlik.org/JA52NN76GE

APA

Mersin, E. Ö., & Bahşi, M. (2025). On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices. Journal of New Results in Science, 14(3), 237-256. https://doi.org/10.54187/jnrs.1705030

AMA

1.Mersin EÖ, Bahşi M. On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices. JNRS. 2025;14(3):237-256. doi:10.54187/jnrs.1705030

Chicago

Mersin, Efruz Özlem, and Mustafa Bahşi. 2025. “On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices”. Journal of New Results in Science 14 (3): 237-56. https://doi.org/10.54187/jnrs.1705030.

EndNote

Mersin EÖ, Bahşi M (December 1, 2025) On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices. Journal of New Results in Science 14 3 237–256.

IEEE

[1]E. Ö. Mersin and M. Bahşi, “On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices”, JNRS, vol. 14, no. 3, pp. 237–256, Dec. 2025, doi: 10.54187/jnrs.1705030.

ISNAD

Mersin, Efruz Özlem - Bahşi, Mustafa. “On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices”. Journal of New Results in Science 14/3 (December 1, 2025): 237-256. https://doi.org/10.54187/jnrs.1705030.

JAMA

1.Mersin EÖ, Bahşi M. On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices. JNRS. 2025;14:237–256.

MLA

Mersin, Efruz Özlem, and Mustafa Bahşi. “On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices”. Journal of New Results in Science, vol. 14, no. 3, Dec. 2025, pp. 237-56, doi:10.54187/jnrs.1705030.

Vancouver

1.Efruz Özlem Mersin, Mustafa Bahşi. On the Commutators and Anti-Commutators of Matrix Functions Involving Exchange Matrices. JNRS. 2025 Dec. 1;14(3):237-56. doi:10.54187/jnrs.1705030