eigenvalue (plural eigenvalues)
- (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 .
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.