Volume 4 • Issue 1 • PP: 21-29 • 2022
On Some Novel Results About Neutrosophic Square Complex Matrices
Open Access & Copyright
© 2022 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Abstract
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.
Keywords
References
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
Cite This Article
Choose your preferred format
Publisher's Note
The statements, opinions, and data presented in this article are solely those of the author(s) and do not necessarily represent those of ASPG, the journal, or its editors. ASPG and the editors disclaim responsibility for any harm arising from the use of any ideas, methods, instructions, or products described in this article, to the fullest extent permitted by applicable law.