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Eigenspace vs Eigenvector - What's the difference?

eigenspace | eigenvector | Related terms |

Eigenvector is a related term of eigenspace.



In linear algebra terms the difference between eigenspace and eigenvector

is that eigenspace is a set of the eigenvectors associated with a particular eigenvalue, together with the zero vector while eigenvector is a vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context.

eigenspace

English

Noun

(en noun)
  • (linear algebra) A set of the eigenvectors associated with a particular eigenvalue, together with the zero vector.

    • eigenvector

    English

    Noun

    (wikipedia eigenvector) (en noun)
  • (linear algebra) A vector that is not rotated under a given linear transformation; a left or right eigenvector depending on context.
  • (physics, engineering) A right eigenvector; a nonzero vector x such that, for a particular matrix A, A x = \lambda x for some scalar \lambda which is its eigenvalue and an eigenvalue of the matrix.

    • Synonyms

    * latent vector, proper vector

    Related terms

    * eigendecomposition * eigenfunction * eigenspace * eigenvalue

    See also

    * Mathworld article on eigenvectors ----