# Eigenvalues and eigenvectors

## Vectors that map to their scalar multiples, and the associated scalars / From Wikipedia, the free encyclopedia

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In linear algebra, an **eigenvector** (/ˈaɪɡənˌvɛktər/) or **characteristic vector** of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding **eigenvalue**, often denoted by , is the factor by which the eigenvector is scaled.

Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed.[1] Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.