Eigenfunction

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function ${\displaystyle f}$ in that space that, when acted upon by D, is only multiplied by some scaling factor called an eigenvalue. As an equation, this condition can be written as

for some scalar eigenvalue ${\displaystyle \lambda .}$ The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

An eigenfunction is a type of eigenvector.