# Eigenvalues and Normalised Eigenvectors

## Homework Statement

I have a matrix
H= [h g
g h]
and I need to find the eigenvalues and normalised eigenvectors

## The Attempt at a Solution

I subtracted lamda from the diagonal and then solved for the determinant equally zero. The eigenvalues I found were
(h-lambda)^2=g^2
so (h-lambda)=+/- g
lamdba=h+/-g

but I'm not sure how to find the normalised eigenvectors?

Homework Helper
After finding the eigenvalues, plug them back into the equation (A - λ I)x = 0, one by one, to get your eigenvectors. Then normalize them.

Thank you very much.

So what I have done is
for eigenvalue h+g I have two equations
hx+gy=hx+gx and gx+hy = hy+gy which gives x=y so eigenvalue h+g has eigenvector (1,1)
and for eigenvalue h-g I have two equations
hx+gy=hx-gx and hx+gy=hy-gy so x=-y so eigenvalue h-g has eigenvector (1,-1)

Is that correct?

are these normalised?