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Mathematics-Online lexicon:

Eigenvalue, Eigenvector, Eigenspace

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A scalar $ \lambda$ is called eigenvalue of square matrix $ A$ if

$\displaystyle A v = \lambda v,\quad v\ne 0\,. $

The vectors $ v \neq 0$ with $ Av = \lambda v$ are called eigenvectors associated with eigenvalue $ \lambda$. The set of the zero vector and of all eigenvectors associated with a given eigenvalue forms a vector space called eigenspace $ V_\lambda$ of $ \lambda$.

see also:

[Examples]
  automatically generated 6/25/2018