# How to solve eigenvalues from a characteristic equation.

Discussion in 'Homework Help' started by u-will-neva-no, Nov 5, 2011.

1. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
Hey! I have worked out the characteristic equation using det(A-λI) = 0,
where
(ignore the line, it is a matrix but don't know how to do it in LaTex so used the fraction function)

So my characteristic equation is:

where and

How would I solve the eigenvalues for the above function? I understand that it is the values of but not sure how to make the function to to zero in this general case... Thanks!

Jul 7, 2009
1,577
142
Your characteristic equation in is a quadratic -- can't you just write down the two roots (eigenvalues) using the quadratic formula? I get . As always, check the geezer's algebra. u-will-neva-no likes this.
3. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2

My complete question is the following. I need to obtain a relationship between the trace and the determinant of A. The question also talks about a formula
A = M (M^-1) Would it be possible if anyone could explain/ give a solid example on how to use this formula?

4. ### Georacer Moderator

Nov 25, 2009
5,154
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u-will-neva-no likes this.
5. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
@someonesdad, I think I was wrong to expand out and your form is alot better to deal with. Has anyone come across a problem like this before?

6. ### Georacer Moderator

Nov 25, 2009
5,154
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I agree with someonesdad's answer too. It's not that unusual of a problem. The methodology to set up your equation is standard. The fact that in the end you get a quadratic equation shouldn't trouble you, it's pretty common.

7. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
What I don't understand Is how I can find the eigenvectors when my two eigenvalues are messy. Can the above eigenvalues be expressed in a matrix form?

8. ### Georacer Moderator

Nov 25, 2009
5,154
1,281

Which makes your eigenvectors the solutions of the equation:

I know it's fuzzy, but remember that in the end λi is a constant for your use.

u-will-neva-no likes this.
9. ### u-will-neva-no Thread Starter Member

Mar 22, 2011
230
2
Cool, thanks Georacer!