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If I take a infinite-dimensional square matrix, what can I say about its eigenvalue spectrum? Will they have a discrete infinity of eigenvalues or continuous infinity of them?

Qmechanic
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SRS
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    discussed in many other questions, see e.g.: http://physics.stackexchange.com/q/95193/ http://physics.stackexchange.com/q/68639/ (for normalizability) http://physics.stackexchange.com/q/98462/ (for the definition of different bases - defines the infinite dimensional matrix) – Martin Feb 13 '14 at 07:53

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Infinite matrices, if properly handled, are nothing but linear operators (either bounded or unbounded) on the Hilbert space $\ell^2(\mathbb N)$. So they can have point spectrum, continuous spectrum, residual spectrum just in view of the general theory of operators in general Hilbert spaces.

Valter Moretti
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