Editing Eigenfunction (section)

{{short description|Mathematical function of a linear operator}}
[[File:Drum vibration mode12.gif|right|frame|This solution of the [[vibrations of a circular drum|vibrating drum problem]] is, at any point in time, an eigenfunction of the [[Laplace operator]] on a disk.]]
In [[mathematics]], an '''eigenfunction''' of a [[linear map|linear operator]] ''D'' defined on some [[function space]] is any non-zero [[function (mathematics)|function]] <math>f</math> in that space that, when acted upon by ''D'', is only multiplied by some scaling factor called an [[eigenvalues and eigenvectors|eigenvalue]]. As an equation, this condition can be written as
<math display="block">Df = \lambda f</math>
for some [[scalar (mathematics)|scalar]] eigenvalue <math>\lambda.</math>{{sfn|Davydov|1976|p=20}}{{sfn|Kusse|Westwig|1998|p=435}}{{sfn|Wasserman|2016}} The solutions to this equation may also be subject to [[Boundary value problem#boundary value conditions|boundary conditions]] that limit the allowable eigenvalues and eigenfunctions.

An eigenfunction is a type of [[eigenvalues and eigenvectors|eigenvector]].