The spectrum of a projection is contained in $\{0, 1\}$, as $$(\lambda I-P)^{-1} = \frac{1}{\lambda} ( I - P) +\frac{1}{\lambda-1 }P$$Only $0$ and $1$ can be an eigenvalue of a projection, the corresponding eigenspaces are the range and kernel of the projection. wikipedia
What is the above equation called? How is it obtained?