The corollary says that if α=β, f has to be a multiple of the identity function (or unit matrix).

For the proof one looks at an eigenvalue λ

_{i}. And subtracts the following on both sides:

This changes to:

Now we apply the Schur's Lemma from last time and find out that has to be either invertible or the 0 function. But it cannot be invertible because λ

_{i}is an eigenvalue (actually the only eigenvalue). And we have what we wanted.

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