English

Noun

eigenvalue ‎(plural eigenvalues)

1. (linear algebra) A scalar, , such that there exists a vector (the corresponding eigenvector) for which the image of under a given linear operator is equal to the image of under multiplication by ; i.e.

   The eigenvalues of a square transformation matrix may be found by solving .

Usage notes

When unqualified, as in the above example, eigenvalue conventionally refers to a right eigenvalue, characterised by for some right eigenvector . Left eigenvalues, charactarised by also exist with associated left eigenvectors . For commutative operators, the left eigenvalues and right eigenvalues will be the same, and are referred to as eigenvalues with no qualifier.

Synonyms

• characteristic root
• characteristic value
• eigenroot
• latent value
• proper value

Related terms

• eigen decomposition
• eigenface
• eigenfunction
• eigenmode
• eigenstate
• eigenvector

Translations

See also

• eigenvalue on Wikipedia.Wikipedia
• Mathworld article on eigenvalues