Solving Eigenvalues of Hessian Matrix

[Firepanda]

g(x,y) = x^3 - 3x^2 + 5xy -7y^2

Hessian Matrix =

6x-6******5

5********-7

Now I have to find the eigenvalues of this matrix, so I end up with the equation (where a = lambda)

(6x - 6 - a)(-7 - a) - 25 = 0

Multiplying out I get:

a^2 - 6xa + 13a - 42x + 17 = 0

How am I supposed to solve for a? Usually I just use the quadratic formula for my eigenvalues..

Should I take a third row/ column for my hessian matrix?

 

[D H]

First off, you have a numerical error in your Hessian. Double check your derivation.

To find the eigenvalues, just solve for a as you would normally (i.e., the eigenvalues will be functions of x).

 

[Firepanda]

http://img229.imageshack.us/img229/2286/hesssn5.jpg

That's the whole question, I assume I'm doing something wrong because my roots of the quadratic for lamba is very complicated.

And yes thankyou I changed my -7 value in my hessian for -14

 

[D H]

So, what is H(0,0)?

 

[Firepanda]

So, what is H(0,0)?

I've no idea :D this is the 1st hessian question I've ever done, i also previosuly made a thread in the same section about what this notation meant, because I'm not too sure.

Do I just plug in x= 0 and y=0?

So my hessian would be:

-6*****5

5*****-14