For the given matrix
2 0 -2
0 -1 0
-2 0 -1
I want to find eigenvectors with a length of 1.
So the eigenvalues are -1,-2,3
solving for each one i got x=0, z=0 for -1
x,y,z = 0 for -2
and x = -2z, y=0 for 3
so i guess the only eigenvector with length 1 would be the when the norm of the last solution equals to 1?
Nonsense! The definition of "eigenvalue" is that there exist a non-zero vector such that Av= lambda v.
You can find a non-zero eigenvector for each eigenvalue. Divide each by its norm to get length 1.and x = -2z, y=0 for 3
so i guess the only eigenvector with length 1 would be the when the norm of the last solution equals to 1?