Hessian

Calculus · Formula · Not yet linked from a lesson

Hij=∂2f∂xi ∂xjH_{ij} = \frac{\partial^2 f}{\partial x_i \, \partial x_j}

The matrix of second derivatives, describing curvature rather than slope. Its eigenvalues say whether a flat point is a minimum, a maximum or a saddle — and in high dimensions, saddles are what you actually hit.

Symbols

HH
The Hessian matrix, symmetric for well-behaved functions.
∂2\partial^2
A second partial derivative.
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