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International Journal of Neutrosophic Science

Volume 24 , Issue 1 , PP: 94-103, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5

Mayada Abualhomos 1 , Ahmed Atallah Alsaraireh 2 , Malik Bataineh 3 , Nabeela Abu-Alkishik 4 , Isra Al-Shbeil 5 , Abdallah Al-Husban 6 *

  • 1 Applied Science Private University Amman,11931, Jordan - (abuhomos@asu.edu.jo)
  • 2 Department of Computer Information Systems, The University of Jordan – Aqaba, Jordan - (a.alsarairah@ju.edu.jo)
  • 3 Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan - (msbataineh@just.edu.jo)
  • 4 Department of Mathematics, Jerash University, Jerash, Jordan - (Nabeelakishik@yahoo.com)
  • 5 Department of Mathematics, Faculty of Sciences, University of Jordan, Amman 11942, Jordan - (i.shbeil@ju.edu.jo)
  • 6 Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan - (dralhosban@inu.edu.jo)

    • Doi: https://doi.org/10.54216/IJNS.240109

    Received: August 26, 2023 Revised: December 12, 2023 Accepted: March 28, 2024
    Abstract

    This paper will study the necessary conditions and sufficient conditions for the problem of orthogonality in 4-plithogenic and 5-plithogenic vector spaces, where we provided a definition of the real scalar products defined above these spaces, and we used the new concept of scalar product that was defined in determining the necessary and sufficient condition for the orthogonality of symbolic 4-plithogenic and 5-plithogenic vectors, in addition to calculating various norms and their metric properties. We have also provided some examples that aim to explain the scientific contribution of this work.

    Keywords :

    plithogenic vector space , inner product , plithogenic norm , orthogonal basis , ortho-normed vectors.

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    Cite This Article As :
    Abualhomos, Mayada. , Atallah, Ahmed. , Bataineh, Malik. , Abu-Alkishik, Nabeela. , Al-Shbeil, Isra. , Al-Husban, Abdallah. On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. International Journal of Neutrosophic Science, vol. , no. , 2024, pp. 94-103. DOI: https://doi.org/10.54216/IJNS.240109
    Abualhomos, M. Atallah, A. Bataineh, M. Abu-Alkishik, N. Al-Shbeil, I. Al-Husban, A. (2024). On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. International Journal of Neutrosophic Science, (), 94-103. DOI: https://doi.org/10.54216/IJNS.240109
    Abualhomos, Mayada. Atallah, Ahmed. Bataineh, Malik. Abu-Alkishik, Nabeela. Al-Shbeil, Isra. Al-Husban, Abdallah. On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. International Journal of Neutrosophic Science , no. (2024): 94-103. DOI: https://doi.org/10.54216/IJNS.240109
    Abualhomos, M. , Atallah, A. , Bataineh, M. , Abu-Alkishik, N. , Al-Shbeil, I. , Al-Husban, A. (2024) . On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. International Journal of Neutrosophic Science , () , 94-103 . DOI: https://doi.org/10.54216/IJNS.240109
    Abualhomos M. , Atallah A. , Bataineh M. , Abu-Alkishik N. , Al-Shbeil I. , Al-Husban A. [2024]. On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. International Journal of Neutrosophic Science. (): 94-103. DOI: https://doi.org/10.54216/IJNS.240109
    Abualhomos, M. Atallah, A. Bataineh, M. Abu-Alkishik, N. Al-Shbeil, I. Al-Husban, A. "On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5," International Journal of Neutrosophic Science, vol. , no. , pp. 94-103, 2024. DOI: https://doi.org/10.54216/IJNS.240109

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