On left spectrum of a split quaternionic matrix

Abstract

In noncommutative and nondivision algebra, left spectrum of matrices are less known and is not easy to handle. Split quaternion algebra is a noncommutative and nondivision algebra. In this paper, by the formulas of solving the equations ax = b and ax 2 + bx + c = 0 over split quaternions, we make an attempt to understand the left spectrum of a split quaternion matrix of order 2.