An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12

Abuobida M. A.; Barbara; Raja Abdullah; Yaser Ahmad; Husain

doi:https://doi.org/10.54216/IJNS.220204

Full Length Article

Volume 22 • Issue 2 • PP: 35-53 • 2023

An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12

Abuobida M. A. Alfahal ^1*

mail

,

Barbara Charchekhandra ²

mail

,

Raja Abdullah Abdulfatah ¹

mail

,

Yaser Ahmad Alhasan ¹

mail

,

Husain Alhayek ³

mail

¹Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia

²Jadavpur University, Department of Mathematics, Kolkata, India

³Hama University, Department of Mathematics, Hama, Syria

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.220204

format_quote Cite this article

Received: June 28, 2023 Revised: August 19, 2023 Accepted: September 28, 2023

View PDF open_in_new

Abstract

The concept of symbolic n-plithogenic algebraic matrices as symmetric structures with n+1 symmetric classical components with the special definition of the multiplication operation. This paper is dedicated to studying the properties of symbolic 10, and 9-plithogenic real square matrices and 11, 12-plithogenic real matrices from algebraic point of view, where algorithms for computing the eigenvalues and determinants will be proved. Also, the inverse of a symbolic n-plithogenic matrix for the special values n=10, n=9, n=11, and n=12 will be presented.

Keywords

symbolic 9-plithogenic matrix symbolic 10-plithogenic matrix symbolic 11-plithogenic matrix symbolic 12-plithogenic matrix symbolic plithogenic eigenvalue symbolic plithogenic eigenvector.

References

[1] Abobala, M., Hatip, A., and Bal, M., " A Review On Recent Advantages In Algebraic Theory Of Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol.17, 2021.

[2] Abobala, M. On Refined Neutrosophic Matrices and Their Applications in Refined Neutrosophic Algebraic Equations. J. Math. 2021, 2021, 5531093.

[3] Merkepci, M., and Abobala, M., " On Some Novel Results About Split-Complex Numbers, The Diagonalization Problem And Applications To Public Key Asymmetric Cryptography", Journal of Mathematics, Hindawi, 2023.

[4] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic Equations, Journal Of Mathematics, Hindawi, 2021

[5] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of neutrosophic Science, Vol. 16, pp. 72-79, 2021.

[6] Merkepci, H., and Abobala, M., " On The Symbolic 2-Plithogenic Rings", International Journal of Neutrosophic Science, 2023.

[7] Smarandache, F., " Introduction to the Symbolic Plithogenic Algebraic Structures (revisited)", Neutrosophic Sets and Systems, vol. 53, 2023.

[8] Taffach, N., and Ben Othman, K., " An Introduction to Symbolic 2-Plithogenic Modules Over Symbolic 2-Plithogenic Rings", Neutrosophic Sets and Systems, Vol 54, 2023.

[9] Taffach, N., " An Introduction to Symbolic 2-Plithogenic Vector Spaces Generated from The Fusion of Symbolic Plithogenic Sets and Vector Spaces", Neutrosophic Sets and Systems, Vol 54, 2023.

[10] Ali, R., and Hasan, Z., "An Introduction To The Symbolic 3-Plithogenic Vector Spaces", Galoitica Journal Of Mathematical Structures and Applications, vol. 6, 2023.

[11] Ben Othman, K., "On Some Algorithms For Solving Symbolic 3-Plithogenic Equations", Neoma Journal Of Mathematics and Computer Science, 2023.

[12] Merkepci, H., and Rawashdeh, A., " On The Symbolic 2-Plithogenic Number Theory and Integers ", Neutrosophic Sets and Systems, Vol 54, 2023.

[13] Rawashdeh, A., "An Introduction To The Symbolic 3-plithogenic Number Theory", Neoma Journal Of Mathematics and Computer Science, 2023.

[14] Alfahal, A.; Alhasan, Y.; Abdulfatah, R.; Mehmood, A.; Kadhim, M. On Symbolic 2-Plithogenic Real Matrices and Their Algebraic Properties. Int. J. Neutrosophic Sci. 2023, 21.

[15] Merkepci, H., "On Novel Results about the Algebraic Properties of Symbolic 3-Plithogenic and 4-Plithogenic Real Square Matrices", Symmetry, MDPI, 2023.

[16] Hatip, A., " On The Algebraic Properties of Symbolic n-Plithogenic Matrices For n=5, n=6", Galoitica Journal of Mathematical Structures and Applications, 2023.

[17] Merkepci, M., Abobala, M., and Allouf, A., " The Applications of Fusion Neutrosophic Number Theory in Public Key Cryptography and the Improvement of RSA Algorithm ", Fusion: Practice and Applications, 2023.

[18] Merkepci, M., and Abobala, M., " Security Model for Encrypting Uncertain Rational Data Units Based on Refined Neutrosophic Integers Fusion and El Gamal Algorithm ", Fusion: Practice and Applications, 2023.

[19] Abobala, M., and Allouf, A., " On A Novel Security Scheme for The Encryption and Decryption Of 2×2 Fuzzy Matrices with Rational Entries Based on The Algebra of Neutrosophic Integers and El-Gamal Crypto-System", Neutrosophic Sets and Systems, vol.54, 2023.

[20] Ben Othman, K., Von Shtawzen, O., Khaldi, A., and Ali, R., "On The Concept Of Symbolic 7-Plithogenic Real Matrices", Pure Mathematics For Theoretical Computer Science, Vol.1, 2023.

[21] Ben Othman, K., Von Shtawzen, O., Khaldi, A., and Ali, R., "On The Symbolic 8-Plithogenic Matrices", Pure Mathematics For Theoretical Computer Science, Vol.1, 2023.

[22] M. B. Zeina, N. Altounji, M. Abobala, and Y. Karmouta, “Introduction to Symbolic 2-Plithogenic Probability Theory,” Galoitica: Journal of Mathematical Structures and Applications, vol. 7, no. 1, 2023.

[23] Ali, R., and Hasan, Z., "An Introduction To The Symbolic 3-Plithogenic Vector Spaces", Galoitica Journal Of Mathematical Structures and Applications, vol. 6, 2023.

[24] Sankari, H., and Abobala, M., "Neutrosophic Linear Diophantine Equations With two Variables", Neutrosophic Sets and Systems, Vol. 38, pp. 22-30, 2020.

[25] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic Sets and Systems, Vol. 45, 2021.

[26] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021.

[27] Nader Mahmoud Taffach , Ahmed Hatip., "A Review on Symbolic 2-Plithogenic Algebraic Structures " Galoitica Journal Of Mathematical Structures and Applications, Vol.5, 2023.

[28] Nader Mahmoud Taffach , Ahmed Hatip.," A Brief Review on The Symbolic 2-Plithogenic Number Theory and Algebraic Equations ", Galoitica Journal Of Mathematical Structures and Applications, Vol.5, 2023.

[29] Agboola, A.A.A., Akinola, A.D., and Oyebola, O.Y., " Neutrosophic Rings I" , International J.Mathcombin, Vol 4,pp 1-14. 2011

[30] Smarandache, F., and Ali, M., "Neutrosophic Triplet Group", Neural. Compute. Appl. 2019.

[31] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings", Neutrosophic sets and systems, Vol. 45, 2021.

[32] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal of Mathematics and Mathematical Sciences, hindawi, 2021

[33] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.

Cite This Article

Choose your preferred format

format_quote

Alfahal, Abuobida M. A., Charchekhandra, Barbara, Abdulfatah, Raja Abdullah, Alhasan, Yaser Ahmad, Alhayek, Husain. "An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12." International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 2, 2023, pp. 35-53. DOI: https://doi.org/10.54216/IJNS.220204

Alfahal, A., Charchekhandra, B., Abdulfatah, R., Alhasan, Y., Alhayek, H. (2023). An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12. International Journal of Neutrosophic Science, Volume 22(Issue 2), 35-53. DOI: https://doi.org/10.54216/IJNS.220204

Alfahal, Abuobida M. A., Charchekhandra, Barbara, Abdulfatah, Raja Abdullah, Alhasan, Yaser Ahmad, Alhayek, Husain. "An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12." International Journal of Neutrosophic Science Volume 22, no. Issue 2 (2023): 35-53. DOI: https://doi.org/10.54216/IJNS.220204

Alfahal, A., Charchekhandra, B., Abdulfatah, R., Alhasan, Y., Alhayek, H. (2023) 'An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12', International Journal of Neutrosophic Science, Volume 22(Issue 2), pp. 35-53. DOI: https://doi.org/10.54216/IJNS.220204

Alfahal A, Charchekhandra B, Abdulfatah R, Alhasan Y, Alhayek H. An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12. International Journal of Neutrosophic Science. 2023;Volume 22(Issue 2):35-53. DOI: https://doi.org/10.54216/IJNS.220204

A. Alfahal, B. Charchekhandra, R. Abdulfatah, Y. Alhasan, H. Alhayek, "An Approach To Symbolic n-Plithogenic Square Real Matrices For 9≤ n ≤12," International Journal of Neutrosophic Science, vol. Volume 22, no. Issue 2, pp. 35-53, 2023. DOI: https://doi.org/10.54216/IJNS.220204

Digital Archive Ready