eigenelement

Noun

Meaning

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}

.

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