Algebraic techniques for Maxwell's equations in commutative quaternionic electromagnetics

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 parallel to A alpha - alpha lambda parallel to(F) = min 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.