## eigenvector## English## Noun( 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* |
## eigenvalue## English## 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!- ”The
**eigenvalues**lambda!of a square transformation matrix rm M!may be found by solving det({rm M} – lambda {rm I}) = 0!.
## Usage notesWhen unqualified, as in the above example, 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* ( |

## 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.