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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 22 , Issue 4 , PP: 56-62, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

A Note on Invertible Neutrosophic Square Matrices

P. Prabakaran 1 * , Gustavo Alvarez G´omez 2 , Rita Azucena Diaz Vasquez 3 , Andr´es Le´on Yacelga 4

  • 1 Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam, Erode - 638401, Tamil Nadu, India - (prabakaranpvkr@gmail.com)
  • 2 Universidad Regional Aut´onoma de los Andes (UNIANDES), Ecuador - (rectorado@uniandes.edu.ec)
  • 3 Universidad Regional Aut´onoma de los Andes (UNIANDES), Ecuador - (ui.ritadiaz@uniandes.edu.ec)
  • 4 Universidad Regional Aut´onoma de los Andes (UNIANDES), Ecuador - (ui.andresleon@uniandes.edu.ec)

    • Doi: https://doi.org/10.54216/IJNS.220405

    Received: May 24, 2023 Revised: July 07, 2023 Accepted: November 01, 2023
    Abstract

    The purpose of this article is to study the adjoint and inverse of neutrosophic matrices, where the inverse of a neutrosophic square matrix is defined and studied in terms of neutrosophic determinant and neutrosophic adjoint. It is shown by examples that, the converse part of the result “M is invertible if and only if detM ̸= 0” is not true, proved by Mohammad Abobala et al. in.2 Also some of the properties of neutrosophic adjoint are discussed.

    Keywords :

    Neutrosophic matrix , neutrosophic adjoint , neutrosophic determinant , neutrosophic inverse.

    References

    [1] Abobala, M., “Neutrosophic Real Inner Product Spaces”, Neutrosophic Sets and Systems, Vol. 43, 2021.

    [2] 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.

    [3] Abobala, M., “On Some Neutrosophic Algebraic Equations”, Journal of New Theory, Vol. 33, 2020.

    [4] Abobala, M., “On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations”, Journal of Mathematics, Hindawi, 2021.

    [5] Abobala, M., “A Study of Nil Ideals and Kothe’s Conjecture in Neutrosophic Rings”, International Journal of Mathematics and Mathematical Sciences, Hindawi, 2021.

    [6] Akram, M., “Single-Valued Neutrosophic Graphs”, Infosys Science Foundation Series in Mathematical Sciences, Springer, 2018.

    [7] Chalapathi, T., and Madhavi, L., “Neutrosophic boolean rings”, Neutrosophic Sets and Systems, vol. 33, pp. 57–66, 2020.

    [8] Das, R., Smarandache, F., and Tripathy, B., “Neutrosophic Fuzzy Matrices and Some Algebraic Operations”, Neutrosophic Sets and Systems, Vol. 32, pp. 401-409, 2020.

    [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] Edalatpanah, S. A., “Systems of neutrosophic linear equations”, Neutrosophic Sets and Systems, vol. 33, pp. 92–104, 2020.

    [11] Kandasamy,W. B. V., and Smarandache, F., “Some Neutrosophic Algebraic Structures and Neutrosophic n-Algebraic Structures”’, (Arizona: Hexis Phoenix), 2006.

    [12] Khaled, H., and Younus, A., and Mohammad, A., “The Rectangle Neutrosophic Fuzzy Matrices”, Faculty of Education Journal Vol. 15, 2019. (Arabic version)

    [13] Sankari, H., and Abobala, M., “Neutrosophic Linear Diophantine Equations With two Variables”, Neutrosophic Sets and Systems, Vol. 38, 2020.

    [14] Smarandache, F., “Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets”, Inter. J. Pure Appl. Math., pp. 287-297, 2005.

    [15] Smarandache, F., “Introduction to Neutrosophic Statistics”, USA: Sitech and Education Publishing, 2014.

    Cite This Article As :
    Prabakaran, P.. , Alvarez, Gustavo. , Azucena, Rita. , Le´on, Andr´es. A Note on Invertible Neutrosophic Square Matrices. International Journal of Neutrosophic Science, vol. , no. , 2023, pp. 56-62. DOI: https://doi.org/10.54216/IJNS.220405
    Prabakaran, P. Alvarez, G. Azucena, R. Le´on, A. (2023). A Note on Invertible Neutrosophic Square Matrices. International Journal of Neutrosophic Science, (), 56-62. DOI: https://doi.org/10.54216/IJNS.220405
    Prabakaran, P.. Alvarez, Gustavo. Azucena, Rita. Le´on, Andr´es. A Note on Invertible Neutrosophic Square Matrices. International Journal of Neutrosophic Science , no. (2023): 56-62. DOI: https://doi.org/10.54216/IJNS.220405
    Prabakaran, P. , Alvarez, G. , Azucena, R. , Le´on, A. (2023) . A Note on Invertible Neutrosophic Square Matrices. International Journal of Neutrosophic Science , () , 56-62 . DOI: https://doi.org/10.54216/IJNS.220405
    Prabakaran P. , Alvarez G. , Azucena R. , Le´on A. [2023]. A Note on Invertible Neutrosophic Square Matrices. International Journal of Neutrosophic Science. (): 56-62. DOI: https://doi.org/10.54216/IJNS.220405
    Prabakaran, P. Alvarez, G. Azucena, R. Le´on, A. "A Note on Invertible Neutrosophic Square Matrices," International Journal of Neutrosophic Science, vol. , no. , pp. 56-62, 2023. DOI: https://doi.org/10.54216/IJNS.220405

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