aspg-21-1285-1791472330 20261008151210 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2022 19 1 Mohammad Abobala Tishreen University, Faculty Of Science, Department Of Mathematics, Latakia, Syria M. Bisher Ziena Aleppo University, Faculty Of Science, Department Of Statistics, Aleppo, Syria R. Iqbal Doewes R. Iqbal Doewes Zahraa Hussein AL-Mustaqbal University College, Physical Education And Sport Sciences Department, Hillah, Babil, Iraq The aim of this paper is to solve the problem of representing refined neutrosophic matrices by linear functions, where it describes the structure of refined neutrosophic linear transformations that represent refined neutrosophic matrices. On the other hand, this work introduces a novel algorithm to compute a basis of any refined neutrosophic vector space depending on the classical basis of its corresponding classical vector space. 2022 342 349 1285 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.190131 https://www.americaspg.com/journal/21/article/1285 https://www.americaspg.com/storage/1709.pdf