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Title

On Some Novel Results About Neutrosophic Square Complex Matrices

  Ahmad Salama 1 * ,   Rasha Dalla 2 ,   Malath Al Aswad 3 ,   Rozina Ali 4

1  Department of Mathematics, port said, Egypt
    (drsalama44@gmail.com)

2  Departement of Mathematics, Albaath University, Homs, Syria
    (rasha.dallah20@gmail.com)

3  PHD of Mathematics, GaziAntep, Turkey
    (Malaz.Aswad@yahoo.com)

4  Department Of Mathematics, Cairo University, Egypt
    (rozyyy123n@gmail.com)


Doi   :   https://doi.org/10.54216/JNFS.040103

Received: April 13, 2022 Accepted: August 15, 2022

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 :

Neutrosophic complex matrix , neutrosophic real number , neutrosophic determinant , neutrosophic inverse

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


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MLA Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. "On Some Novel Results About Neutrosophic Square Complex Matrices." Full Length Article, Vol. 4, No. 1, 2022 ,PP. 21-29 (Doi   :  https://doi.org/10.54216/JNFS.040103)
APA Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). On Some Novel Results About Neutrosophic Square Complex Matrices. Journal of Full Length Article, 4 ( 1 ), 21-29 (Doi   :  https://doi.org/10.54216/JNFS.040103)
Chicago Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. "On Some Novel Results About Neutrosophic Square Complex Matrices." Journal of Full Length Article, 4 no. 1 (2022): 21-29 (Doi   :  https://doi.org/10.54216/JNFS.040103)
Harvard Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). On Some Novel Results About Neutrosophic Square Complex Matrices. Journal of Full Length Article, 4 ( 1 ), 21-29 (Doi   :  https://doi.org/10.54216/JNFS.040103)
Vancouver Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. On Some Novel Results About Neutrosophic Square Complex Matrices. Journal of Full Length Article, (2022); 4 ( 1 ): 21-29 (Doi   :  https://doi.org/10.54216/JNFS.040103)
IEEE Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali, On Some Novel Results About Neutrosophic Square Complex Matrices, Journal of Full Length Article, Vol. 4 , No. 1 , (2022) : 21-29 (Doi   :  https://doi.org/10.54216/JNFS.040103)