Volume 4 , Issue 1 , PP: 21-29, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Ahmad Salama 1 * , Rasha Dalla 2 , Malath Al Aswad 3 , Rozina Ali 4
Doi: https://doi.org/10.54216/JNFS.040103
The objective of this paper is to study algebraic properties of complex neutrosophic matrices, where a necessary and sufficient condition for the invertibility of a complex square neutrosophic matrix is presented by defining the complex neutrosophic determinant. On the other hand, this work introduces the concept of neutrosophic characteristic polynomial and neutrosophic Cayley-Hamilton theorem for the complex case.
Neutrosophic complex matrix , neutrosophic real number , neutrosophic determinant , neutrosophic inverse
1] Abobala, M., "AH-Subspaces in Neutrosophic Vector Spaces", International Journal of Neutrosophic Science,
Vol. 6 , pp. 80-86. 2020.
[2] Abobala, M.,. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces", International
Journal of Neutrosophic Science", Vol. 9, pp.74-85. 2020.
[3] Sankari, H., and Abobala, M., "Neutrosophic Linear Diophantine Equations With two Variables",
Neutrosophic Sets and Systems, Vol. 38, pp. 22-30, 2020.
[4] Sankari, H., and Abobala, M." n-Refined Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 36,
pp. 1-11. 2020.
[5] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of
neutrosophic science, 2022.
[6]Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set,
Neutrosophic Probability", American Research Press. Rehoboth, 2003.
[7] Suresh, R., and S. Palaniammal,. "Neutrosophic Weakly Generalized open and Closed Sets", Neutrosophic
Sets and Systems, Vol. 33, pp. 67-77,. 2020.
[8] Olgun, N., and Hatip, A., "The Effect Of The Neutrosophic Logic On The Decision Making, in Quadruple
Neutrosophic Theory And Applications", Belgium, EU, Pons Editions Brussels,pp. 238-253. 2020.
[9] Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal
of Neutrosophic Science", Vol. 0, pp. 67-76 . 2019.
[10] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0,
pp. 27-34. 2020.
[11] Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of
Neutrosophic Science", Vol. 7, pp. 74-78. 2020.
[12] Smarandache, F., and Abobala, M., n-Refined neutrosophic Rings, International Journal of Neutrosophic
Science, Vol. 5 , pp. 83-90, 2020.
[13] Abobala, M., On Some Special Substructures of Neutrosophic Rings and Their Properties, International
Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.
[14] Abobala, M., "On Some Special Substructures of Refined Neutrosophic Rings", International Journal of
Neutrosophic Science, Vol. 5, pp. 59-66. 2020.
[15] Sankari, H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic
Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.
[16] Smarandache, F., and Kandasamy, V.W.B., " Finite Neutrosophic Complex Numbers",·Source: arXiv.
2011.
[17] Agboola, A.A.A,. Akwu, A.D,. and Oyebo, Y.T., " Neutrosophic Groups and Subgroups", International .J
.Math. Combin, Vol. 3, pp. 1-9. 2012.
[18] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in
Physics, 143-146, Vol. 4, 2013.
[19] Adeleke, E.O., Agboola, A.A.A.,and Smarandache, F., "Refined Neutrosophic Rings I", International
Journal of Neutrosophic Science, Vol. 2(2), pp. 77-81. 2020.
[20] Hatip, A., and Abobala, M., "AH-Substructures In Strong Refined Neutrosophic Modules", International
Journal of Neutrosophic Science, Vol. 9, pp. 110-116 . 2020.
[21] Smarandache F., and Abobala, M., "n-Refined Neutrosophic Vector Spaces", International Journal of
Neutrosophic Science, Vol. 7, pp. 47-54. 2020.
[22] Sankari, H., and Abobala, M., "Solving Three Conjectures About Neutrosophic Quadruple Vector Spaces",
Neutrosophic Sets and Systems, Vol. 38, pp. 70-77. 2020.
[23] Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II", International
Journal of Neutrosophic Science, Vol. 2(2), pp. 89-94. 2020.
[24] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic
Equations, Journal Of Mathematics, Hindawi, 2021
[25] Abobala, M., A Study of Maximal and Minimal Ideals of n-Refined Neutrosophic Rings, Journal of Fuzzy
Extension and Applications, Vol. 2, pp. 16-22, 2021.
[26] Abobala, M., " Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic
Modules and Strong Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 39, 2021.
[27] Giorgio, N, Mehmood, A., and Broumi, S.," Single Valued neutrosophic Filter", International Journal of
Neutrosophic Science, Vol. 6, 2020.
[28] Chellamani, P., and Ajay, D., "Pythagorean neutrosophic Fuzzy Graphs", International Journal of
Neutrosophic Science, Vol. 11, 2021.
[29] Milles, S, Barakat, M, and Latrech, A., " Completeness and Compactness In Standard Single Valued
neutrosophic Metric Spaces", International Journal of Neutrosophic Science, Vol.12 , 2021.
[30] Abobala, M., "On Some Neutrosophic Algebraic Equations", Journal of New Theory, Vol. 33, 2020.
[31] Abobala, M., On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations,
Journal of Mathematics, Hindawi, 2021.
[32] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined
Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021
[33] Kandasamy V, Smarandache F., and Kandasamy I., Special Fuzzy Matrices for Social Scientists . Printed in
the United States of America,2007, book, 99 pages.
[34] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings",
Neutrosophic Sets and Systems, Vol. 45, 2021.
[35] Abobala, M., Partial Foundation of Neutrosophic Number Theory, Neutrosophic Sets and Systems, Vol. 39
, 2021.
[36] F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of
Information technology, Hanoi, Vietnam, 17th May 2016.
[37] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S. and Akinleye, S.A., "On refined Neutrosophic Vector
Spaces I", International Journal of Neutrosophic Science, Vol. 7, pp. 97-109. 2020.
[38] Ibrahim, M.A., Agboola, A.A.A, Badmus, B.S., and Akinleye, S.A., "On refined Neutrosophic Vector
Spaces II", International Journal of Neutrosophic Science, Vol. 9, pp. 22-36. 2020.
[39] Abobala, M, "n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An Application
To Rings and Modules", International Journal of Neutrosophic Science, Vol. 12, pp. 81-95 . 2020.
[40] Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl.
Math., pp. 287-297. 2005.
[41] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal
of New Theory, vol. 33, 2020.
[42] Abobala, M., Hatip, A., Olgun, N., Broumi, S., Salama, A,A., and Khaled, E, H., The algebraic creativity In
The Neutrosophic Square Matrices, Neutrosophic Sets and Systems, Vol. 40, pp. 1-11, 2021.
[43] Aswad, F, M., " A Study of Neutrosophic Complex Number and Applications", Neutrosophic Knowledge,
Vol. 1, 2020.
[44] Aswad. F, M., " A Study of neutrosophic Bi Matrix", Neutrosophic Knowledge, Vol. 2, 2021.
[45] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, vol. 43, 2021.
[46] Aswad, M., " A Study of The Integration Of Neutrosophic Thick Function", International journal of
neutrosophic Science, 2020.
[47] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal
of Mathematics and Mathematical Sciences, hindawi, 2021.
[48] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module
Homomorphisms", International journal of neutrosophic science, 2022.
[49] Abobala, M., and Hatip, A., "An Algebraic Approach to Neutrosophic Euclidean Geometry", Neutrosophic
Sets and Systems, Vol. 43, 2021.
[50] Aswad, M., " A Study Of neutrosophic Differential Equation By using A Neutrosophic Thick Function",
neutrosophic knowledge, Vol. 1, 2020.
[51] Olgun, N., Hatip, A., Bal, M., and Abobala