What's Hessian matrix ???

[abcdefg10645]

Here are all my problem ~

1. What's Hessian matrix ?

2. How Hessian matrix was derived ?

3. Can u recommend some books about this ?

[Pinu7]

1. I hate latex, so for a function of n variables, f(x1,...,xn) which is differentiable twice the hessian of the function is defined as

http://wpcontent.answers.com/math/7/5/d/75dc4e662a991741dc6d0314b6c8a7d2.png

2. It is a definition, it is not derived, however, there are some cool theorems with it such as an application to critical points.

3. Any GOOD book on multivariable and vector calculus.
EXAMPLES:
http://www.amazon.com/Vector-Calculus-Jerrold-E-Marsden/dp/0716749920/ref=sr_1_1?ie=UTF8&s=books&qid=1256782912&sr=8-1

http://www.amazon.com/VECTOR-CALCULUS-SUSAN-COLLEY/dp/B000N5GZOC/ref=sr_1_3?ie=UTF8&s=books&qid=1256782943&sr=1-3

http://www.amazon.com/Calculus-Vol-Multi-Variable-Algebra-Applications/dp/0471000078/ref=sr_1_1?ie=UTF8&s=books&qid=1256782991&sr=1-1

[abcdefg10645]

To Pinu7~

Thank ur replying ~

And the reason I want to ask Hessian was that I heard that Hessian Matrix can be used while proving Taylor's expension for multivariable

How come is that ??