# Eigenvalues of Infinite Dimensional Matrix [duplicate]

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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?

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## marked as duplicate by Chris White, Brandon Enright, John Rennie, Qmechanic♦Feb 13 '14 at 8:21

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.