Wikipedia:Today's featured article/November 1, 2005

The red vector is an eigenvector of the transformation while the blue one is not

In mathematics, the eigenvalues, eigenvectors, and eigenspaces of a transformation are important properties of this transformation. These key concepts play a major role in mathematics and, in particular, in linear algebra and functional analysis, as well as in numerous applied disciplines. The prefix eigen emphasizes the fact that these properties are important characteristics of the transformation. In many common cases knowing all eigenvalues and eigenvectors of a transformation is equivalent to the explicit knowledge of the transformation. The word eigen is German for "own", "peculiar", or "individual": the most likely translation into English mathematical jargon would be "characteristic", and some older references do use the expressions "characteristic value", "characteristic vector" and so forth, or even "eigenwert" which is German for eigenvalue, but the more distinctive term "eigenvalue" has become standard.

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