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What is meant by the spectrum of a linear operator ##A##? I read somewhere that if ##0## belongs in the spectrum, then ##A## is not invertible. Can anyone finesse this for me?

I read the wikipedia page, but this was tough for me to understand. Perhaps illustrating with a simple example, say ##(Af)(x) = \sin x f(x)##, or ##(Af)(x) = e^x f(x)## or really anything thats easy to understand.