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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?

  • 5
    It seems more convincing to me to note that we have $P^2 = P$, so $P$ satisfies $X(X - 1)$.2012-01-04
  • 0
    Yeah. But I really want to know what that equation is?2012-01-04
  • 2
    If you want a name, it is the "partial fraction decomposition of the resolvent" of $P$.2012-01-04

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