2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135920In this paper we study a symmetry group of vector space. Basis manifold is a homogeneous space of a symmetry group. This concept leads us to the definition of active and passive transformations on basis manifold. Active transformation can be expressed as a transformation of vector space. Passive transformation gives ability to define concepts of invariance and of geometrical object.English text - 15 pages; Russian text - 16 pagesDifferential GeometryGeneral Mathematicstext