What is a Vector Space? How to determine if its a Vector Space or not?
VECTOR SPACES AND SUBSPACES INTRODUCTION The definition of a vector space V , whose elements are called vectors , involves arbitrary filed K , whose elements are called scalars . The following notation will be used (unless otherwise stated or implied) V given vectors space u,v,w vectors in V K given number field a , b , c , or k scalars in K VECTOR SPACES The following define the notion of a vector space V , where K is the field of scalars. Definition: Let V be a nonempty set with two operations: 1. Rule of vector addition , which assigns to any u,v ∈ V a sum u+v in V . 2. Rule of vector multiplication , which assigns to any u ∈ V and k ∈ K a product ku ∈ K . Then V is ...