# Eigenvalue question

1. Nov 1, 2004

### ee7klt

hi,
if an operator O has the property that O^{4}f(x)=f(x), what are the eigenvalues of O? any hints on how to go about this?

2. Nov 1, 2004

### Galileo

Since $O^4$ is the identity, it has all eigenvalues one.
If $O$ has an eigenvector f with eigenvalue $\lambda$, what can you tell about $O^2$