# Jacobian and Hessian Matrices

1. Jul 9, 2011

### YAHA

Can someone direct me to a good deep exposition of Jacobians and Hessians? I am especially looking for stuff that pertains to their being generalizations of derivatives of vector and scalar functions as well as div, grad, curl. Book sources or web links are appreciated.

2. Jul 9, 2011

### hunt_mat

have you tried looking on wikipedia?

3. Jul 9, 2011

### YAHA

Of course. There were a few helpful articles I found.

4. Jul 9, 2011

### Blackforest

Just go to google.your country and try the words: E.B. Christoffel revisited.

You will find very interesting recent works on that topic.

But ...good luck, because its a hard "stuff"

5. Jul 9, 2011

### hunt_mat

The Hessian is essentially a matrix operator that takes functions $f:\mathbb{R}^{n}\rightarrow\mathbb{R}$ and maps them into $\mathbb{R}^{n\times n}$, the element $H_{ij}$ of the matrix are given by:
$$H_{ij}=\frac{\partial^{2}f}{\partial x_{i}\partial x_{j}}$$