Scientific Journal Of King Faisal University
Basic and Applied Sciences
Scientific Journal of King Faisal University / Basic and Applied Sciences
Determinant of a Neutrosophic Matrix
(Eman Alabdullah and Safwan Aouira)Abstract
In this paper, we study some properties of the determinant of a neutrosophic matrix. Also, we prove that |A.adj(A)|=|A|=|adj(A).A| and define the matrices
A_((p_1…p_m |q_1…q_m))and A_((p→q)). Further, a method is presented for calculating the determinant of a neutrosophic matrix that has a large number of columns and rows.
KEYWORDS
adjoint, identity neutrosophic matrix, permutation, principal submatrix, transpose, triangular NM
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References
Dhar, M., Broumi, S. and Smarandache, F. (2014). A note on square neutrosophic fuzzy matrices. Neutrosophic Sets and Systems, 3(n/a), 37–41.
Molodtsov, D. (1999). Soft set theory—first results. Computers and mathematics with applications, 37(4-5), 19–31. DOI: 10.1016/S0898-1221(99)00056-5
Salama, A., Al-Aswad, M., Alqtib, A., Ismael, H., Gaded M., Elhbebib, R. and Yasser, I. (2022). Asasiaat Almasfufat Walmueadalat Altafaduliat Walhandasat fi Almajal Alnaytrusufikaa ‘Fundamentals of Matrices, Differential Equations, and Geometry in the Neutrosophic Field’. Ohio, USA: Educational Publisher. [in Arabic]
Smarandache, F. (1998). Neutrosophy. Neutrosophic Probability, Set, and Logic. ProQuest Information and Learning. Michigan, USA: Ann Arbor.
Smarandache, F. (2006). Neutrosophic set-a generalization of the intuitionistic fuzzy set. In: 2006 IEEE International Conference on Granular Computing. University of New Mexico, Gallup, USA, n/a/05/2006. DOI:10.1109/GRC.2006.1635754
Sophia R.P. and Jayapriya V. (2019). Determinant of a fuzzy neutrosophic matrix. International Journal of Scientific Engineering and Research, 7(5), 54–7.
Sumathi, I.R. and Arockiarani, I. (2014). New operations on fuzzy neutrosophic soft matrices. International journal of innovative Research and Studies, 13(3), 110–24.
Uma, R., Murugadas, P. and Sriram, S. (2017). The determinant and adjoint of fuzzy neutrosophic soft matrices. International Journal of Mathematics and its Application, 5(4), 821–33.
Varol, B.P., Cetkin, V. and Aygün, H. (2019). A new view on neutrosophic matrix. Journal of Hyperstructures, 8(1), 48–57.
Wang, H., Smarandache, F., Zhang, Y. and Sunderraman, R. (2010). Single valued neutrosophic sets. Multispace and Multistructure, 4(n/a), 410–3.
Ҫetkin, V., and Aygün, H. (2015). An approach to neutrosophic subgroup and it,s fundamental properties. Journal of Intelligent and Fuzzy Systems, 29(n/a), 1941–7. DOI: 10.3233/IFS-151672
Ҫetkin, V., and Aygün, H. (2019). A new approach to neutrosophic subrings. Sakarya University Journal of Science, 23(3), 472–7. DOI: 10.16984/saufenbilder.451979
Ҫetkin, V., Varol, B.P. and Aygün, H. (2017). On neutrosophic submodules of a module. Hacettepe Journal of Mathematics and Statistics, 46(5), 791–9. DOI: 10.15672/ HJMS.2017437