Let $M$ be a smooth manifold. A critical point of a map $u:M\to\R$ at $x\in M$ is called non-degenerate if the Hessian matrix $H_u$ (in any local coordinate system) at $x$ is non-degenerate.

A smooth function $u:M\to\R$ is called Morse if all its critical points are non-degenerate. Morse functions exist on any smooth manifold, and in fact form an open dense subset of smooth functions on $M$ (this fact is often phrased ``a generic smooth function is Morse'').