Properties of the matrix from Kronecker product on the representation of quaternion group

Abstract

Abstract This paper discusses the properties of matrices, which are elements of a group derived from the application of Kronecker product to the representation of the quaternion group (the author calls this group with Kronecker quaternion group). The properties of the new matrices constructed by matrices from the Kronecker quaternion group as submatrix in a partitioned matrix are discussed based on transpose, determinant, and permutation matrix.