Important: The linalg package has been deprecated. Use the superseding command VectorCalculus[Hessian], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The procedure hessian(expr, vars) computes the Hessian matrix of expr with respect to vars.

The matrix result is n x n, where n is the length of vars. The (i, j)th entry of the matrix result is diff(expr, vars[i], vars[j]).

The command with(linalg,hessian) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$\mathrm{hessian}\left(xyz\,\left[x\,y\,z\right]\right)$

$\left[\begin{array}{ccc}0& z& y\\ z& 0& x\\ y& x& 0\end{array}\right]$

$\mathrm{hessian}\left(x^{2}y+3x{y}^2\,\left[x\,y\right]\right)$

$\left[\begin{array}{cc}2y& 2x+6y\\ 2x+6y& 6x\end{array}\right]$