If L^~ is a linear operator on a function space, then f is an eigenfunction for L^~ and lambda is the associated eigenvalue whenever L^~f=lambdaf.

Renteln and Dundes (2005) give the following (bad) mathematical joke about eigenfunctions:

Q: What do you call a young eigensheep? A: A lamb, duh!

See also

Eigen Decomposition, Eigenvalue, Eigenvector, Functional

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Renteln, P. and Dundes, A. "Foolproof: A Sampling of Mathematical Folk Humor." Notices Amer. Math. Soc. 52, 24-34, 2005.

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Cite this as:

Weisstein, Eric W. "Eigenfunction." From MathWorld--A Wolfram Web Resource.

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