Eigenvalue

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English

Etymology

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Pronunciation

Noun

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Template:Lb A scalar, λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear operator A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
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Usage notes

When unqualified, as in the above example, eigenvalue conventionally refers to a right eigenvalue, characterised by $M x = λ x$ for some right eigenvector $x$ . Left eigenvalues, characterised by $y M = y λ$ 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

Further reading

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