Hessian matrix of scalar function

`hessian(f,v)`

example

`hessian(`

finds
the Hessian matrix of the scalar function `f`

,`v`

)`f`

with
respect to vector `v`

in Cartesian coordinates.

If you do not specify `v`

, then `hessian(f)`

finds
the Hessian matrix of the scalar function `f`

with
respect to a vector constructed from all symbolic variables found
in `f`

. The order of variables in this vector is
defined by `symvar`

.

Find the Hessian matrix of a function by using `hessian`

.
Then find the Hessian matrix of the same function as the Jacobian
of the gradient of the function.

Find the Hessian matrix of this function of three variables:

syms x y z f = x*y + 2*z*x; hessian(f,[x,y,z])

ans = [ 0, 1, 2] [ 1, 0, 0] [ 2, 0, 0]

Alternatively, compute the Hessian matrix of this function as the Jacobian of the gradient of that function:

jacobian(gradient(f))

ans = [ 0, 1, 2] [ 1, 0, 0] [ 2, 0, 0]

`curl`

| `diff`

| `divergence`

| `gradient`

| `jacobian`

| `laplacian`

| `potential`

| `vectorPotential`

Was this topic helpful?