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This is a question about an off-hand remark from a lecturer a few weeks ago. He was talking about eigenvectors/values of a matrix, and rhetorically asked us if we'd seen the interpretation of eigenvalues as frequencies.

I haven't been able to find a clear explanation for this, and I'd be interested if anyone could enlighten me or (perhaps even more usefully) point me in the direction of a good text which covers this interpretation/application.

Thankyou very much!

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    It only makes sense if your vector space can reasonably be interpreted as modelling oscillations. Otherwise, I don't see why you would gain something by speaking about frequencies instead of eigenvalues. Besides, even when they can be interpreted as frequencies, we still speak about eigenfrequencies of the system to distinguish them from frequencies which are no eigenvalues of the operator under consideration.2012-04-02

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