TY  - JOUR
T1  - Laplace Method for Calculate the Determinant of Cubic-Matrix of Order 2 and Order 3
AU  - Zaka, Orgest
AU  - Salihu, Armend
PY  - 2024
DA  - September
Y2  - 2024
DO  - 10.55549/epstem.1566170
JF  - The Eurasia Proceedings of Science Technology Engineering and Mathematics
JO  - EPSTEM
PB  - ISRES Publishing
WT  - DergiPark
SN  - 2602-3199
SP  - 192
EP  - 209
VL  - 29
LA  - en
AB  - In this paper, as a continuation of our work on the determinants of cubic matrices of order 2 and order 3, we have investigated the possibilities of developing the concept of determinants of cubic matrices with three indexes, as well as the possibility of calculating them using the Laplace expansion method. We have observed that the notion of permutation expansion, which is used for square determinants, and the concept of the Laplace expansion method, which is used for square and non-square (rectangular) determinants, may be applied to this novel concept of 3D determinants. In this research, we demonstrated that the Laplace expansion approach is also applicable to cubic matrices of the second and third orders. These results are presented simply and with extensive proof. The findings are also supported by illustrated cases. In addition, we provided an algorithmic explanation for the Laplace expansion approach applied to cubic matrices.
KW  - Cubic-matrix determinant
KW  - Laplace expansion method
KW  - Permutation method
KW  - Computer algorithm.
CR  - Zaka, O. & Salihu, A. (2024). Laplace method for calculate the determinant of cubic-matrix of order 2 and order 3. The Eurasia Proceedings of Science, Technology, Engineering & Mathematics (EPSTEM), 29, 192-209.
UR  - https://doi.org/10.55549/epstem.1566170
L1  - https://dergipark.org.tr/en/download/article-file/4283668
ER  -