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

Authors : Hasan ÇAKIR, Mustafa ÖZDEMİR

Pages : 518-532

Doi:10.31801/cfsuasmas.991894

View : 13 | Download : 8

Publication Date : 2022-06-30

Article Type : Research Paper

Abstract :Split-complex insert ignore into journalissuearticles values(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 $2x2$ split-complex matrix in three cases : $i:~\Delta=0,~ii:~\Delta\neq0$ and $\Delta$ is not null split-complex number, $iii:~\Delta\neq0$ and $\Delta$ is a null split-complex number where $\Delta=insert ignore into journalissuearticles values(trA);^{2}-4detA$.
Keywords : Split complex numbers, hyperbolic numbers, matrix exponential