Eigenvalue

English

Etymology

From Template:Prefix, a Template:Partial calque.

Pronunciation

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Noun

1. Template:Lb A scalar, $\lambda$, such that there exists a non-zero vector $x$ (a corresponding eigenvector) for which the image of $x$ under a given linear operator $\mathrm{A}$ is equal to the image of $x$ under multiplication by $\lambda$; i.e. $\mathrm{A}x=\lambda x$.

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Usage notes

• When unqualified, as in the above example, eigenvalue conventionally refers to a right eigenvalue, characterised by $\mathrm{M}x=\lambda x$ for some right eigenvector $x$. Left eigenvalues, characterised by $y\mathrm{M}=y\lambda$ also exist with associated left eigenvectors $y$. (In consequence of the equations, left eigenvectors are row vectors, while right eigenvectors are column vectors.) The convention of right eigenvector as "standard" is fundamentally an arbitrary choice.

Synonyms

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Translations

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See also

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Further reading

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