Open AccessThe Commutation Matrices of Elements in Kronecker Quaternion Groups
Author(s) -
Yanita Yanita,
Eka Purwanti,
Lyra Yulianti
Publication year - 2022
Publication title -
jambura journal of mathematics
Language(s) - English
Resource type - Journals
eISSN - 2656-1344
pISSN - 2654-5616
DOI - 10.34312/jjom.v4i1.12004
Subject(s) - permutation matrix , commutation , kronecker product , quaternion , mathematics , group (periodic table) , matrix (chemical analysis) , pure mathematics , algebra over a field , transpose , kronecker delta , abelian group , combinatorics , physics , geometry , quantum mechanics , eigenvalues and eigenvectors , materials science , voltage , circulant matrix , composite material
This article discusses the commutation matrix in the Kronecker quaternion group; that is, a non-abelian group whose 32 elements are matrices of 4 × 4 size, with entries in the set of complex numbers. The purpose of this paper is to describe the commutation matrices obtained in relation to the matrices in this group. The commutation matrix is a permutation matrix that associates the relationship between the vec and vec of the transpose matrix. Based on the classification of matrices in the Kronecker quaternion group, there are 16 classification of commutation matrices for the matrices in this group.