What Are the Key Applications of the Hessian Matrix in Multivariable Calculus?

[abcdefg10645]

What's Hessian matrix ?

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,...,x_n) 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:
https://www.amazon.com/dp/0716749920/?tag=pfamazon01-20

https://www.amazon.com/dp/B000N5GZOC/?tag=pfamazon01-20

https://www.amazon.com/dp/0471000078/?tag=pfamazon01-20

 

[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 ??