eigenelement
التعريفات والمعاني
== English ==
=== Noun ===
eigenelement (plural eigenelements)
(mathematics) A nonzero element
m
{\displaystyle m}
of a semimodule
M
{\displaystyle M}
, such that there exists an endomorphism
A
{\displaystyle A}
on
M
{\displaystyle M}
and a real number
r
{\displaystyle r}
(a corresponding eigenvalue) for which the image of
m
{\displaystyle m}
under
A
{\displaystyle \mathrm {A} }
is equal to the product of
r
{\displaystyle r}
times
m
{\displaystyle m}
; i.e.
m
A
=
r
m
{\displaystyle m{A}=rm}
.
==== Usage notes ====
An eigenelement is a generalization of an eigenvector to a semimodule.