Explicit formulas for exponential of 2×2 split-complex matrices

Abstract

Split-complex (hyperbolic) numbers are ordered pairs of real numbers, written in the form x + jy with j(2) - 1, used to describe the geometry of the Lorentzian plane. Since a null split-complex number does not have an inverse, some methods to calculate the exponential of complex matrices are not valid for split-complex matrices. In this paper, we examined the exponential of a 2 Chi 2 split-complex matrix in three cases : i. triangle = 0, ii. triangle not equal 0 and triangle is not null split-complex number, iii. triangle (sic) 0 and triangle is a null split-complex number where triangle = (trA)(2) - 4 det A.