eigenvectorEnglishNoun(wikipedia eigenvector ) x such that, for a particular matrix A, A x = lambda xfor some scalar lambdawhich is its eigenvalue and an eigenvalue of the matrix. Synonyms* latent vector, proper vector See also* |
eigenvalueEnglishNoun(en noun ) lambda! , such that there exists a vector x(the corresponding eigenvector) for which the image of xunder a given linear operator rm A!is equal to the image of xunder multiplication by lambda; i.e. {rm A} x = lambda x!
Usage notesWhen 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. Synonyms* characteristic root See also* (“eigenvalue” on Wikipedia ) |
Eigenvector vs Eigenvalue – What’s the difference?
Eigenvector vs Eigenvalue - What's the difference?
As nouns the difference between eigenvector and eigenvalue is that eigenvector is (linear algebra) a vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context while eigenvalue is (linear algebra) the change in magnitude of a vector that does not change in direction under a given linear transformation; a scalar factor by which an eigenvector is multiplied under such a transformation.