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EnglishEdit

EtymologyEdit

eigen- +‎ value

PronunciationEdit

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

NounEdit

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 notesEdit

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.

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