can somebody help me understand what the spectrum of a linear map is? from what i have seen its the set of lambdas such that A-I(lambda) is not invertible for a linear map A:X->X, so its a set which makes that operator not invertible, could 0 be in this set? an example would be nice as im struggling to visualise this, thanks
2026-03-26 19:18:43.1774552723
what is the spectrum of a linear map and does 0 belong to it?
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In the finite dimensional case the spectrum is nothing but the set of eigenvalues. The identity matrix is an example of a linear map whose spectrum does not contain $0$.