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

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

The procedure jacobian(f, v) computes the Jacobian matrix of f with respect to v. The (i,j)th entry of the matrix result is $\frac{\partial }{\partial v_j}{f}_i$.

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

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

$A≔\mathrm{vector}\left(\left[x^2\,xy\,xz\right]\right)$

$A≔\left[\begin{array}{ccc}{x}^2& xy& xz\end{array}\right]$

$\mathrm{jacobian}\left(A\,\left[x\,y\,z\right]\right)$

$\left[\begin{array}{ccc}2x& 0& 0\\ y& x& 0\\ z& 0& x\end{array}\right]$