Eigenfunction

Function that is an eigenvector of a linear operator on a function space

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\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 D f = λ f {\displaystyle Df=\lambda f} for some scalar eigenvalue λ . {\displaystyle \lambda .} The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

Nº Q1307821 ★

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Eigenfunction

Function that is an eigenvector of a linear operator on a function space

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\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 D f = λ f {\displaystyle Df=\lambda f} for some scalar eigenvalue λ . {\displaystyle \lambda .} The solutions to this equation may also be subject to boundary conditions that limit the allowable eigenvalues and eigenfunctions.

From Wikipedia

In mathematics, an eigenfunction of a linear operator D defined on some function space is any non-zero function f {\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 D f = λ f {\displaystyle Df=\lambda f} for some scalar eigenvalue λ . {\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.

Text: Wikipédia, CC BY-SA 4.0. · Image: Joroco246 (CC BY-SA 4.0) ·

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