Basis

The basis $X$ for $U$ is a set such that:

• $X$ is Linearly Independent
• $X$ is a Spanning Set of $U$. ($U=span(X)$)

Converting Spanning Sets into Basis

• Remove all dependent columns

Basis Vector Notation

$e_n$ where $n$ is the basis vector in question. $e_1=(1,0,\dots ,0)$

Concepts

• Basis by Unique Representation Theorem
• Multiple Basis for a Single Vector Space