Some new linear representations of matrix quaternions with some applications

Abstract

In this paper, we construct several new attractive and interested linear representations of matrix quaternions by using Kronecker structures in order to obtain the general partitioned linear representation form of matrix quaternions. In addition, we present the general solutions of three important partitioned quaternions systems by using our new representations and Kronecker structure. These systems are: the partitioned linear quaternion equations, general linear matrix quaternion system and coupled Sylvester matrix quaternion system. Keywords: Quaternions, Kronecker product, Schur complement, Moore-Penrose inverse, Linear matrix quaternion equations, 2010 MSC: 11R52, 15A69, 15A24