3
$\begingroup$

What are necessary and sufficient conditions for a matrix-valued function $H: \mathbb{R}^d \rightarrow \mathbb{R}^{d\times{}d}$ to be the Hessian of a scalar function $F:\mathbb{R}^d \rightarrow \mathbb{R}$, i.e. $H(x) = \nabla^2 F(x)$.

Is equality of mixed partials enough?

Another question asks this but requires $F$ to be convex.

$\endgroup$

0

Browse other questions tagged .