= Nondegenerate stationary points of a planar harmonic function
{title2=$\det D^2u=-u_{xx}^2-u_{xy}^2<0$}
For a planar <harmonic function>, $u_{yy}=-u_{xx}$. Its <Hessian matrix> is therefore $\begin{pmatrix}a&b\\b&-a\end{pmatrix}$, with <eigenvalues> $\pm\sqrt{a^2+b^2}$. At a <stationary point> with nonzero <Hessian matrix> <determinant>, both signs occur, so the point is a <saddle point>. A zero determinant requires separate treatment and is not covered by this nondegenerate test. The result is the local quadratic counterpart of the <maximum principle> for <harmonic functions>.
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