eigenelement

English

eigenelement (plural eigenelements)

(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.

单词	eigenelement
释义	eigenelement English Noun eigenelement (plural eigenelements) (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. ${\\displaystyle m{A}=rm}$ . Usage notes An eigenelement is a generalization of an eigenvector to a semimodule.
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