Explicit formulas for exponential of 2×2 split-complex matrices
Yıl: 2022 Cilt: 71 Sayı: 2 Sayfa Aralığı: 518 - 532 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.991894 İndeks Tarihi: 05-09-2022
Explicit formulas for exponential of 2×2 split-complex matrices
Öz: 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 $Delta=(trA)^{2}-4detA$.
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| APA | ÇAKIR H, Ozdemir M (2022). Explicit formulas for exponential of 2×2 split-complex matrices. , 518 - 532. 10.31801/cfsuasmas.991894 |
| Chicago | ÇAKIR Hasan,Ozdemir Mustafa Explicit formulas for exponential of 2×2 split-complex matrices. (2022): 518 - 532. 10.31801/cfsuasmas.991894 |
| MLA | ÇAKIR Hasan,Ozdemir Mustafa Explicit formulas for exponential of 2×2 split-complex matrices. , 2022, ss.518 - 532. 10.31801/cfsuasmas.991894 |
| AMA | ÇAKIR H,Ozdemir M Explicit formulas for exponential of 2×2 split-complex matrices. . 2022; 518 - 532. 10.31801/cfsuasmas.991894 |
| Vancouver | ÇAKIR H,Ozdemir M Explicit formulas for exponential of 2×2 split-complex matrices. . 2022; 518 - 532. 10.31801/cfsuasmas.991894 |
| IEEE | ÇAKIR H,Ozdemir M "Explicit formulas for exponential of 2×2 split-complex matrices." , ss.518 - 532, 2022. 10.31801/cfsuasmas.991894 |
| ISNAD | ÇAKIR, Hasan - Ozdemir, Mustafa. "Explicit formulas for exponential of 2×2 split-complex matrices". (2022), 518-532. https://doi.org/10.31801/cfsuasmas.991894 |
| APA | ÇAKIR H, Ozdemir M (2022). Explicit formulas for exponential of 2×2 split-complex matrices. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71(2), 518 - 532. 10.31801/cfsuasmas.991894 |
| Chicago | ÇAKIR Hasan,Ozdemir Mustafa Explicit formulas for exponential of 2×2 split-complex matrices. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71, no.2 (2022): 518 - 532. 10.31801/cfsuasmas.991894 |
| MLA | ÇAKIR Hasan,Ozdemir Mustafa Explicit formulas for exponential of 2×2 split-complex matrices. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.71, no.2, 2022, ss.518 - 532. 10.31801/cfsuasmas.991894 |
| AMA | ÇAKIR H,Ozdemir M Explicit formulas for exponential of 2×2 split-complex matrices. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(2): 518 - 532. 10.31801/cfsuasmas.991894 |
| Vancouver | ÇAKIR H,Ozdemir M Explicit formulas for exponential of 2×2 split-complex matrices. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2022; 71(2): 518 - 532. 10.31801/cfsuasmas.991894 |
| IEEE | ÇAKIR H,Ozdemir M "Explicit formulas for exponential of 2×2 split-complex matrices." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 71, ss.518 - 532, 2022. 10.31801/cfsuasmas.991894 |
| ISNAD | ÇAKIR, Hasan - Ozdemir, Mustafa. "Explicit formulas for exponential of 2×2 split-complex matrices". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 71/2 (2022), 518-532. https://doi.org/10.31801/cfsuasmas.991894 |
