eigenelement

English

Noun

eigenelement (plural eigenelements)

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

Usage notes

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