Eigenfunction

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, an eigenfunction of a <a href="/facts/Linear_map/Q1PBKNVV">linear operator</a> D defined on some <a href="/facts/Function_space/lLUE2R1t">function space</a> is any non-zero <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> 
 
 
 
 f
 
 
 {\displaystyle f}
 
 in that space that, when acted upon by D, is only multiplied by some scaling factor called an <a href="/facts/Eigenvalues_and_eigenvectors/8TjEoT8u">eigenvalue</a>. As an equation, this condition can be written as

 
 
 
 D
 f
 =
 λ
 f
 
 
 {\displaystyle Df=\lambda f}

for some <a href="/facts/Scalar_(mathematics)/MkDbA4Eo">scalar</a> eigenvalue 
 
 
 
 λ
 .
 
 
 {\displaystyle \lambda .}
 
 The solutions to this equation may also be subject to <a href="/facts/Boundary_value_problem/QEfmUqmP">boundary conditions</a> that limit the allowable eigenvalues and eigenfunctions.
An eigenfunction is a type of <a href="/facts/Eigenvalues_and_eigenvectors/8TjEoT8u">eigenvector</a>.

Eigenfunction open-in-new

Eigenfunction