Thread: Orthogonal matrices

i have found two eigenvalues for a matrix i've been working on, both are lambda = 2...

when i substitute the eigenvalue back into the matrix and row reduce i get

y= 0 and x = z

so i said my first eigenvector, V1 is a 3*1 column matrix with entries 1, 0, 1.

My problem is finding the 2nd eigenvector...

I need to find a vector V2 such that V1.V2 = 0 and V2 (hat) = 1.

I think i need another vector V3 as well which is orthogonal to V1 and V2 and is itself a unit vector.. Does this mean i should have a 3rd eigenvalue?

Im using these vectors as columns of matrix O...

Delete this thread please Mods, i reposted the question using LaTex as i think my wording here was a bit messy

Sorry if any hassle caused

Tekken