What Are the Best Resources for Understanding Jacobian and Hessian Matrices?

[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.

 

[hunt_mat]

have you tried looking on wikipedia?

 

[YAHA]

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

 

[member 11137]

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"

 

[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:
$$H_{ij}=\frac{\partial^{2}f}{\partial x_{i}\partial x_{j}}$$