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)
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.
References :
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| Style | # |
|---|---|
| MLA | Mayada Abualhomos, Ahmed Atallah Alsaraireh, Malik Bataineh, Nabeela Abu-Alkishik, Isra Al-Shbeil, Abdallah Al-Husban. "On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5." International Journal of Neutrosophic Science, Vol. 24, No. 1, 2024 ,PP. 94-103 (Doi : https://doi.org/10.54216/IJNS.240109) |
| APA | Mayada Abualhomos, Ahmed Atallah Alsaraireh, Malik Bataineh, Nabeela Abu-Alkishik, Isra Al-Shbeil, Abdallah Al-Husban. (2024). On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. Journal of International Journal of Neutrosophic Science, 24 ( 1 ), 94-103 (Doi : https://doi.org/10.54216/IJNS.240109) |
| Chicago | Mayada Abualhomos, Ahmed Atallah Alsaraireh, Malik Bataineh, Nabeela Abu-Alkishik, Isra Al-Shbeil, Abdallah Al-Husban. "On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5." Journal of International Journal of Neutrosophic Science, 24 no. 1 (2024): 94-103 (Doi : https://doi.org/10.54216/IJNS.240109) |
| Harvard | Mayada Abualhomos, Ahmed Atallah Alsaraireh, Malik Bataineh, Nabeela Abu-Alkishik, Isra Al-Shbeil, Abdallah Al-Husban. (2024). On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. Journal of International Journal of Neutrosophic Science, 24 ( 1 ), 94-103 (Doi : https://doi.org/10.54216/IJNS.240109) |
| Vancouver | Mayada Abualhomos, Ahmed Atallah Alsaraireh, Malik Bataineh, Nabeela Abu-Alkishik, Isra Al-Shbeil, Abdallah Al-Husban. On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5. Journal of International Journal of Neutrosophic Science, (2024); 24 ( 1 ): 94-103 (Doi : https://doi.org/10.54216/IJNS.240109) |
| IEEE | Mayada Abualhomos, Ahmed Atallah Alsaraireh, Malik Bataineh, Nabeela Abu-Alkishik, Isra Al-Shbeil, Abdallah Al-Husban, On The Real Inner Products and Orthogonality for Plithogenic Vector Spaces of Orders 4 and 5, Journal of International Journal of Neutrosophic Science, Vol. 24 , No. 1 , (2024) : 94-103 (Doi : https://doi.org/10.54216/IJNS.240109) |