TY  - JOUR
TI  - Explicit formulas for exponential of  2×2  split-complex matrices
AB  - 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  $2x2$ split-complex matrix in three cases : $i:~Delta=0,~ii:~Deltaneq0$ and $Delta$ is not null split-complex number, $iii:~Deltaneq0$ and $Delta$ is a null split-complex number where $Delta=(trA)^{2}-4detA$.
AU  - ÇAKIR, Hasan
AU  - Ozdemir, Mustafa
DO  - 10.31801/cfsuasmas.991894
PY  - 2022
JO  - Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
VL  - 71
IS  - 2
SN  - 1303-5991
SP  - 518
EP  - 532
DB  - TRDizin
UR  - http://search/yayin/detay/1118377
ER  -