# eigenvectors and orthogonal matrix

• Apr 7th 2010, 04:15 AM
Tekken
eigenvectors and orthogonal matrix
$\displaystyle A = \left[\begin{matrix}-3 & 0 & 5 \\ 0 & 2 & 0 \\ 5 & 0 & -3\end{matrix}\right]$

I have found the eigenvalues for the above matrix to be, $\displaystyle \lambda = 2$, it occurs twice.

When i plug my eigenvalue of 2 back into the matrix to find the eigenvectors i get;
$\displaystyle y=0, x = z$

So i said my chose my first eigenvector, v1 to be;

$\displaystyle A = \left[\begin{matrix}1 \\ 0 \\ 1 \end{matrix}\right]$

Trouble is i need another 2 vectors V2 and V3 such that:
v1.v2 = 0
v1.v3 = 0
v2.v3 = 0
where v1, v2, v3 are all unit vectors.

Im hoping to find the matrix O where v1,v2,v3 are O's columns

I posted this question earlier but i think its phrasing was a bit messy so i tried using LaTex for the first time...
• Apr 7th 2010, 10:14 AM
qmech
I agree with your first eigenvalue=2 and eigenvector=(1,0,1).
Can you see the other 2 sets,
eigenvalue =2, eigenvector = (0,1,0)
eigenvalue =-8, eigenvector = (1,0,-1)?