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International Journal of Advances in Applied Computational Intelligence

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Online: 2833-5600
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Continuous publication

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Open access journal. All articles are freely available online with no APC.

International Journal of Advances in Applied Computational Intelligence
Full Length Article

Volume 6Issue 2PP: 37-45 • 2024

On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm

Hasan Sankari 1* ,
Mohammad Abobala 1
1Tishreen University, Faculty of Science, Department of Mathematics, Latakia, Syria
* Corresponding Author.
Received: November 15, 2023 Revised: February 2, 2024 Accepted: July 1, 2024

Abstract

This paper is concerned with studying the matrix computations of 3-cyclic refined neutrosophic matrices and 4-cyclic refined neutrosophic matrices with 3cyclic/4-cyclic real entries, where we introduce a novel method to compute eigenvalues and vectors of these matrix classes. Also, we provide a novel algorithm for diagonalization these matrices and to determine whether an n-cyclic refined matrix is diagonalizable or not for n=3, 4.

Keywords

3-cyclic refined matrix 4-cyclic refined matrix Diagonalization problem Matrix computation Eigenvalue

References

[1]   Basheer, A., Ahmad, K., and Ali, R., “A Short Contribution to Von Shtawzen's Abelian Group in n-Cyclic Refined Neutrosophic Rings", Journal of Neutrosophic and Fuzzy Systems, 2022.

[2]  Von Shtawzen, O., “Conjectures for Invertible Diophantine Equations of 3-Cyclic and 4-Cyclic Refined Integers", Journal of Neutrosophic and Fuzzy Systems, Vol.3, 2022.

[3]    Von Shtawzen, O., “On a Novel Group Derived from a Generalization of Integer Exponents and Open Problems", Galoitica journal Of Mathematical Structures and Applications, Vol 1, 2022.

[4]   Basheer, A., Ahmad, K., and Ali, R., “On Some Open Problems about n-Cyclic Refined Neutrosophic Rings and Number Theory", Journal of Neutrosophic and Fuzzy Systems, 2022.

[5]  Alrida Basheer, Katy D. Ahmad, Rozina Ali., "Examples on Some Novel Diophantine Equations Derived from the Group of Units Problem in n-Cyclic Refined Neutrosophic Rings of Integers", Galoitica Journal of Mathematical Structures and Applications, Vol.3, 2022.

[6]  Sankari, H., and Abobala, M., “On the Group of Units Classification In 3-Cyclic and 4-cyclic Refined Rings of Integers and the Proof of Von Shtawzens' Conjectures", International Journal of Neutrosophic Science, 2023.

[7]  Sankari, H., and Abobala, M., “On the Classification of the Group of Units of Rational and Real 2-Cyclic Refined Neutrosophic Rings", Neutrosophic Sets and Systems, 2023.

[8]  Sankari, H., and Abobala, M., “On the Algebraic Homomorphisms between Symbolic 2-Plithogenic Rings And 2 cyclic Refined Rings", Neutrosophic Sets and Systems, 2023.

[9]  Sankari, H. Abobala, M. (2023). On a Generalization of RSA Crypto-system by using 2-Cyclic Refined Integers. Journal of Cybersecurity and Information Management, 12(1), 67-73. DOI:https://doi.org/10.54216/JCIM.120106

[10]  Abobala, M., Sankari, H., & Zeina, M. (2024). On novel security systems based on the 2-cyclic refined integers and the foundations of 2-cyclic refined number      theory. Journal of Fuzzy Extension and Applications, 5(1), 69-85. DOI: 10.22105/jfea.2024.423818.1321

[11] Abobala, M., “n-Cyclic Refined Neutrosophic Algebraic Systems of Sub-Indeterminacies, an Application to Rings and Modules", International Journal of         Neutrosophic Science, 2020.

[12]    Aswad, M., "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices", Neutrosophic Knowledge, 2021.

[13]    Ali, R., "n-Cyclic Refined Neutrosophic Groups", International Journal of Neutrosophic Science, 2021.

[14] Rama Asad Nadweh, Rozina Ali, Maretta Sarkis, "On the Algebraic Properties of 2-Cyclic Refined Neutrosophic Matrices and the Diagonalization Problem",   Neutrosophic Sets and Systems, Vol 54, 2023.

[15]    Sadiq. B., “A Contribution To The group Of Units Problem in Some 2-Cyclic Refined Neutrosophic Rings ", International Journal of Neutrosophic Science, 2022.

[16] Nabil Khuder Salman, Maikel Leyva Vazquez,Batista Hernández Noel. On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von   Shtawzen's Group. International Journal of Neutrosophic Science, (2024); 23 (2): 26-31.

[17] Ahmad Salama, Rasha Dalla, Malath Al Aswad, Rozina Ali. (2022). Some Results About 2-Cyclic Refined Neutrosophic Complex Numbers. Journal of Neutrosophic and Fuzzy Systems, 4 (1), 41 DOI:  https://doi.org/10.54216/JNFS.040105

[18]   Al Basheer, O., “On Some Novel Simplex Linear Codes Defined over the Algebraic Ring f2+vf2", Neoma Journal of Mathematics and Computer Science, 2023.

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Sankari, Hasan, Abobala, Mohammad. "On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm." International Journal of Advances in Applied Computational Intelligence, vol. Volume 6, no. Issue 2, 2024, pp. 37-45. DOI: https://doi.org/10.54216/IJAACI.060204
Sankari, H., Abobala, M. (2024). On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm. International Journal of Advances in Applied Computational Intelligence, Volume 6(Issue 2), 37-45. DOI: https://doi.org/10.54216/IJAACI.060204
Sankari, Hasan, Abobala, Mohammad. "On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm." International Journal of Advances in Applied Computational Intelligence Volume 6, no. Issue 2 (2024): 37-45. DOI: https://doi.org/10.54216/IJAACI.060204
Sankari, H., Abobala, M. (2024) 'On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm', International Journal of Advances in Applied Computational Intelligence, Volume 6(Issue 2), pp. 37-45. DOI: https://doi.org/10.54216/IJAACI.060204
Sankari H, Abobala M. On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm. International Journal of Advances in Applied Computational Intelligence. 2024;Volume 6(Issue 2):37-45. DOI: https://doi.org/10.54216/IJAACI.060204
H. Sankari, M. Abobala, "On The Computational Properties of 3-Cyclic and 4-Cyclic Refined Matrices and the Diagonalization Algorithm," International Journal of Advances in Applied Computational Intelligence, vol. Volume 6, no. Issue 2, pp. 37-45, 2024. DOI: https://doi.org/10.54216/IJAACI.060204
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