International Journal of Advances in Applied Computational Intelligence

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https://doi.org/10.54216/IJAACI

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Volume 6 , Issue 2 , PP: 37-45, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

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

Hasan Sankari 1 , Mohammad Abobala 2

  • 1 Tishreen University, Faculty of Science, Department of Mathematics, Latakia, Syria - (Hasansankari2@gmail.com)
  • 2 Tishreen University, Faculty of Science, Department of Mathematics, Latakia, Syria - (Mohammadabobala777@gmail.com)
  • Doi: https://doi.org/10.54216/IJAACI.060204

    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.

    Cite This Article As :
    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. , no. , 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, (), 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 , no. (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 , () , 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. (): 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, vol. , no. , pp. 37-45, 2024. DOI: https://doi.org/10.54216/IJAACI.060204