eigenvalue

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English[edit]

Etymology[edit]

eigen- +‎ value

Pronunciation[edit]

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

Noun[edit]

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[edit]

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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