التحويلات الخطية النيوتروسوفيكية ونظرية الرتبة والبطلان (أو نظرية الرتبة والإلغاء)

الملخص

In this paper, we investigate neutrosophic linear transformation defined over finite-dimensional vector space.  We rigorously formulate the concepts of the neutrosophic kernel (ker(T_I)) and neutrosophic image (Im(T_I)).establishing their underlying vector space properties.  Based on these definition, we introduce the notions of neutrosophic rank and neutrosophic nullity as the dimensions of the respective subspaces over the neutrosophic field R(I).  The primary contribution of this work is the formulation and proof of the Neutrosophic Rank-Nullity Theorem, extending the fundamental classical result of linear algebra to the neutrosophic domain: dim(V(I))= Rank(T_I )+ Nullity(T_I ).  Finally, several non-trivial concrete examples involving geometric transformations and neutrosophic matrix spaces are presented to illustrate the operational mechanics and validate the theoretical framework established in this study