Here's the follow up post to Schur's Lemma, in case you were anxiously awaiting it.
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 λi. 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 λi is an eigenvalue (actually the only eigenvalue). And we have what we wanted.
Cyclobutanone Prediction Challenge
-
How well can nonadiabatic dynamics forecast an experiment? In brief: The
philosopher of science Imre Lakatos proposed that we should judge a
research progr...
2 days ago
No comments:
Post a Comment