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 $${\displaystyle Df=\lambda f}$$ for some scalar eigenvalue ${\displaystyle \lambda .}$^[1][2][3] 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.