https://doi.org/10.1140/epjp/s13360-022-02794-5
Regular Article
Algebraic techniques for Maxwell’s equations in commutative quaternionic electromagnetics
1
Institute of Mathematics and Information Science, North-Eastern Federal University, 677000, Yakutsk, Russia
2
School of Mathematics and Statistics, Linyi University, 276005, Linyi, Shandong, People’s Republic of China
3
School of Mathematics and Statistics, Heze University, 274015, Heze, Shandong, People’s Republic of China
c
vasvasil@mail.ru
d
jiangtongsong@sina.com
Received:
6
April
2022
Accepted:
29
April
2022
Published online:
12
May
2022
The Maxwell’s equations of commutative quaternions play an important role in commutative quaternion electromagnetism. This paper studies the problem of solutions to Maxwell’s equations of commutative quaternions by means of a real representation of commutative quaternion matrices. This paper first derives an algebraic technique for finding solutions of the least squares eigen-problem 
of the commutative quaternion matrix and also gives algebraic technique for finding the eigenvalues and corresponding eigenvectors of the commutative quaternion matrix. A numerical experiment is provided to demonstrate the feasibility of the real representation algorithm.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
