Last modified on 25 April 2015, at 17:36




eigen- +‎ value


  • enPR: īʹgən'vălyo͞o, IPA(key): /ˈaɪɡənˌvæljuː/
  • (file)


eigenvalue (plural eigenvalues)

  1. (linear algebra) A scalar, \lambda\!, such that there exists a vector x (the corresponding eigenvector) for which the image of x under a given linear operator \rm A\! is equal to the image of x under multiplication by \lambda; i.e. {\rm A} x = \lambda x\!
    The eigenvalues \lambda\! of a square transformation matrix \rm M\! may be found by solving \det({\rm M} - \lambda {\rm I}) = 0\! .

Usage notesEdit

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


Related termsEdit


See alsoEdit