The concept of **basis** is closely connected to the idea of linear independence.

A vector set is a basis for a space if it:

- spans the space, and
- is linearly independent.

**The basis of the subspace**

If any subspace **basis** for the subspace

Said a different way, if a set of vectors forms the basis of a subspace

Think about the basis of a subspace as the smallest, or minimum, set of vectors that can span the subspace. There are no “redundant” or “unnecessary” vectors in the set.

**Standard basis**
You can pick any two linearly independent vectors in

We call the standard basis of