Explicit formulas for exponential of 2×2 split-complex matrices
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
Split-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
.
Description
Keywords
Split-complex numbers, hyperbolic numbers, matrix exponential