# Eigenvalues of Infinite Dimensional Matrix [duplicate]

This question already has an answer here:

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?

-

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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

discussed in many other questions, see e.g.: physics.stackexchange.com/q/95193 physics.stackexchange.com/q/68639 (for normalizability) physics.stackexchange.com/q/98462 (for the definition of different bases - defines the infinite dimensional matrix) – Martin Feb 13 '14 at 7:53

## 1 Answer

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.

-