Let \(F\colon M\to N\) be a smooth map between smooth manifolds. The rank of \(F\) at a point \(p\in M\) is the rank of the total derivative \(dF_p\) in local coordinates.
The function \(F\) has constant rank \(r\) if the rank of \(F\) is equal in every point. We write \(\rank F = r\).
The function F has full rank at a point \(p\in M\) if it coincides with the upper bound for the rank of \(dF_p\). If \(F\) has full rank at every point we just say it has full rank.