Suppose that $S=\set{\vectorlist{v}{n}}\subseteq\complex{m}$ is a set of vectors and $A$ is the $m\times n$ matrix whose columns are the vectors in $S$. Let $B$ be a matrix in reduced row-echelon form that is row-equivalent to $A$ and let $r$ denote the number of pivot columns in $B$. Then $S$ is linearly independent if and only if $n=r$.