Volume 16 , Issue 2 , PP: 72-79, 2021 | Cite this article as | XML | Html | PDF | Full Length Article
Necati Olgun 1 * , Ahmed Hatip 2 , Mikail Bal 3 , Mohammad Abobala 4
Doi: https://doi.org/10.54216/IJNS.160202
This work is dedicated to study the conditions of diagonalization in the case of refined neutrosophic matrices, where it presents the necessary and sufficient conditions for the diagonalization of these matrices by finding a relationship with classical diagonalization of matrices. Also, it describes an algorithm to obtain all eigen values and eigen vectors of refined neutrosophic matrices from the classical ones.
Refined neutrosophic matrix, refined neutrosophic eigen value, refined neutrosophic eigen vector, refined neutrosophic diagonalization
[1] Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II", International Journal of Neutrosophic Science, Vol. 2, pp. 89-94, 2020.
[2] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 45, 2021.
[3] Abobala, M., "On Some Neutrosophic Algebraic Equations", Journal of New Theory, Vol. 33, 2020.
[4] Abobala, M., " On Refined Neutrosophic Matrices and Their Application In Refined Neutrosophic Algebraic Equations", Journal Of Mathematics (Hindawi), 2021.
[5] M. Ali, F. Smarandache, M. Shabir and L. Vladareanu, "Generalization of Neutrosophic Rings and Neutrosophic Fields," Neutrosophic Sets and Systems, vol. 5, pp. 9-14, 2014.
[6] Abobala, M., and Hatip, A., "AH-Substructures In Strong Refined Neutrosophic Modules", International Journal of Neutrosophic Science, Vol. 9, pp. 110-116 , 2020.
[7] Agboola, A.A.A., “On Reļ¬ned Neutrosophic Algebraic Structures”, Neutrosophic Sets and Systems,Vol.10, pp. 99-101, 2015.
[8] Abobala, M., On The Representation Of Neutrosophic Matrices By Neutrosophic Linear Transformations", Journal Of Mathematics (Hindawi), 2021.
[9]Dhar M., Broumi S.,and Smarandache F., "A Note on Square Neutrosophic Fuzzy Matrices", Neutrosophic Sets and Systems'', Vol. 3, pp. 37-41 2014.
[10] Khaled, H., and Younus, A., and Mohammad, A., " The Rectangle Neutrosophic Fuzzy Matrices", Faculty of Education Journal Vol. 15, 2019. (Arabic version).
[11] 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.
[12] W. B. V. Kandasamy and F. Smarandache, Neutrosophic Rings, Hexis, Phoenix, Arizona: Infinite Study, 2006.
[13] Sankari, H., and Abobala, M.," AH-Homomorphisms In Neutrosophic Rings and Refined Neutrosophic Rings", Neutrosophic Sets and Systems, Vol. 38, 2020.
[14] Sankari, H., and Abobala, M., "n-Refined Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 36 , 2020.
[15] Sankari, H., and Abobala, M.," Neutrosophic Linear Diophantine Equations With two Variables", Neutrosophic Sets and Systems, Vol. 38, 2020.
[16] F. Smarandache, Introduction to Neutrosophic Statistics, USA: Sitech & Education Publishing, 2014.
[17] Abobala, M., "Partial Foundation of Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 39 , 2021.
[18] Abobala, M., " Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic Modules and Strong Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 39, 2021.
[19] T.Chalapathi and L. Madhavi,. "Neutrosophic Boolean Rings", Neutrosophic Sets and Systems, Vol. 33, pp. 57-66, 2020.
[20] S. A. Edalatpanah., " Systems of Neutrosophic Linear Equations", Neutrosophic Sets and Systems, Vol. 33, pp. 92-104, 2020.
[21] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021
[22] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021
[23] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.
[24] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal of New Theory, vol. 33, 2020..
[25] Abobala, M., and Hatip, A., "An Algebraic Approch To Neutrosophic Euclidean Geometry", Neutrosophic Sets and Systems, Vol. 43, 2021.
[26] Abobala, M., " A Review On Recent Developments Of Neutrosophic Matrix Theory and Open Problems", Hal-archives, 2021. .
[27] 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.
[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] Es, Haydar, A., "A Note On neutrosophic Soft Menger Topological Spaces", International Journal of Neutrosophic Science, Vol.7, 2020.
[31] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.
[32] Ali, Rozina., " Neutrosophic Matrices and Their Properties", researchgat.net, 2021.
[33] 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.
[34] Ali, R., "A Short Note On The Solution of n-Refined Neutrosophic Linear Diophantine Equations", International Journal Of Neutrosophic Science, Vol. 15, 2021.
