Ok everybody, it's been awhile since I've taken linear algebra. I need some help dusting off the cobwebs. (I'm trying to follow this in a paper; this isn't a homework question, but I'll be glad to move it...)(adsbygoogle = window.adsbygoogle || []).push({});

Let's say I have a matrix M = \begin{bmatrix}

-σ & σ & 0 \\[0.3em]

ρ & -1 & 0 \\[0.3em]

0 & 0 & -1

\end{bmatrix} \

Ok, now I want to find the eigenvectors (I've already found the eigenvalues.

These are λ_1=-1 and λ_2,3 = -(σ+1)/2 +/- ( (σ+1)^2 -4σ(1-ρ))^.5

Now, to find the eigenvectors, I solve these equations:

(-σ-λ)e_1 +σ e_2 =0

ρ e_1 +(-1-λ) e_2 =0

(-1-λ) e_3 =0

Now, I see that the eigenvector for λ_1 is ( 0 0 1).

Now I'm stuck. How do I find the eigenvectors for the other two?

The result in the paper I'm reading says

λ_2,3 = (σ σ+λ_2 0 ) , (σ σ+λ_3 0 )

I forget how to do this....

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# Reminder on how to find eigenvectors

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