Let $\left\{v_{1}, \ldots, v_{n}\right\}$ be a set of elements of a vector space $V$. Let $r\leq n$. We shall say that $\left\{v_{1}, \ldots, v_{r}\right\}$ is a maximal subset of linearly independent elements if $v_{1}, \ldots, v_{r}$ are linearly independent, and if in addition, given any $v_{i}$ with $i>r$, the elements $v_{1}, \ldots, v_{r}, v_{i}$ are linearly dependent. The number of elements $r$ of the maximal is the the maximum number of [[linearly independent vectors]]