### 2.50.3 Hessian matrix : `hessian`

`hessian` takes two arguments : an expression F of n real variables and a vector of these variable names.
`hessian` returns the hessian matrix of F, that is the matrix of the derivatives of order 2.
Example
Find the hessian matrix of F(x,y,z)=2x2y−xz3.
Input :

`hessian(2*x```^```2*y-x*z```^```3 , [x,y,z])`

Output :

`[[4*y,4*x,-(3*z```^```2)],[2*2*x,0,0],[-(3*z```^```2),0,x*3*2*z]]`

To have the hessian matrix at the critical points, first input :

`solve(derive(2*x```^```2*y-x*z```^```3,[x,y,z]),[x,y,z])`

Output is the critical points :

`[[0,y,0]]`

Then, to have the hessian matrix at this points, input :

`subst([[4*y,4*x,-(3*z```^```2)],[2*2*x,0,0], [-(3*z```^```2),0,6*x*z]],[x,y,z],[0,y,0])`

Output :

`[[4*y,4*0,-(3*0```^```2)],[4*0,0,0],[-(3*0```^```2),0,6*0*0]]`

and after simplification :

`[[4*y,0,0],[0,0,0],[0,0,0]]`