eigenelement

eigenelement (plural eigenelements)

1. (mathematics) A nonzero element ${\displaystyle m}$ of a semimodule ${\displaystyle M}$, such that there exists an endomorphism ${\displaystyle A}$ on ${\displaystyle M}$ and a real number ${\displaystyle r}$ (a corresponding eigenvalue) for which the image of ${\displaystyle m}$ under ${\displaystyle \mathrm {A} }$ is equal to the product of ${\displaystyle r}$ times ${\displaystyle m}$; i.e. ${\displaystyle m{A}=rm}$.

An eigenelement is a generalization of an eigenvector to a semimodule.