Rank of a Vector-Valued Function

Statements

Definition. Let $U\subset {\mathbb{R}}^n$ be an open set and $F:U\to {\mathbb{R}}^m$ be a vector-valued function composed of diffeomorphisms. Then, $DF(p)$ is said to have rank $k$ at $p\in U$ if the Jacobian Matrix has rank $k$.

References

1. @Boo75 pp. 47