Çakır, Hasan2022-12-272022-12-272022https://doi.org/10.31801/cfsuasmas.991894http://hdl.handle.net/20.500.12575/86497Split-complex (hyperbolic) numbers are ordered pairs of real numbers, written in the form x + j y 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 x 2 split-complex matrix in three cases : i : Δ = 0 , i i : Δ ≠ 0 and Δ is not null split-complex number, i i i : Δ ≠ 0 and Δ is a null split-complex number where Δ = ( t r A ) 2 − 4 d e t A .enSplit-complex numbers, hyperbolic numbers, matrix exponentialArticle7125185321303-5991