Basis
Definition: The vectors v1, v2,..., vk in a vector space V are said to form a basis for V if (a) v1, v2,..., vk span V and (b) v1, v2,..., vk are linearly independent.
Note*
If v1, v2,..., vk form a basis for a vector space V, then they must be distinct and nonzero.
Note**
The above definition not only applies to a finite set of vectors, but also to an infinite set of vectors in a vector space.
