= Nondegenerate critical point
A <critical point> of a real <function> with continuous second <partial derivatives> is nondegenerate when its <Hessian matrix> is an <invertible matrix> there, equivalently when none of its <eigenvalues> is zero. A <positive-definite matrix> gives a strict <local minimum>, a <negative definite> <Hessian> gives a strict <local maximum>, and opposite-sign <eigenvalues> give a <saddle point of a scalar function>. A nondegenerate <critical point> need not be an extremum: $x^2-y^2$ has <Hessian matrix> $\operatorname{diag}(2,-2)$, which is an <invertible matrix>.
Such critical points are the local building blocks of <Morse theory>.
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