Online Algebra Calculator

Many of users do not use powerful **Maxima computer algebra system** for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only.
To do this job, it is not useful to download the whole application from a web site.

Sponsored links:
Algebra eBooks

The Hessian matrix is the square matrix of second-order partial derivatives of a function.

Given the function:

f(ax^{2} + bxy)

in maxima:

`f(x,y):=(a*x^2 + b*x*y);`

if all second partial derivatives of `f`

exist, then the Hessian matrix of `f`

is the matrix:

H_{f}(x)_{i,j} =

H(f) =

H(f) =

Second partial derivatives

xx =

xy =

yx=

yy =

In maxima

```
```xx:diff(diff(f(x,y),x),x);

xy:diff(diff(f(x,y),x),y);

yx:diff(diff(f(x,y),y),x);

yy:diff(diff(f(x,y),y),y);

In Calculator
Hessian matrix of a function `f(a*x^2 + b*x*y)`

is:

In Maxima:

`hesM:matrix([xx,xy],[yx,yy]);`

Maxima function hessian

`hessian((a*x^2 + b*x*y),[x,y]);`

Diference of maxima function Hessian and our example.

`hesM-hessian((a*x^2 + b*x*y),[x,y]);`