What is the difference between eigenfunctions and eigenvectors of an operator?

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What is the difference between the eigenfunctions and eigenvectors of an operator, for example Laplace-Beltrami operator?

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1 Answer

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An eigenfunction is an eigenvector that is also a function. Thus, an eigenfunction is an eigenvector but an eigenvector is not necessarily an eigenfunction. For example, the eigenvectors of differential operators are eigenfunctions but the eigenvectors of finite-dimensional linear operators are not.

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