# Eigenvalues and eigenvectors

In linear algebra, an eigenvector (/ˈɡənˌvɛktər/) 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 ${\displaystyle \lambda }$,[1] 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.[2] Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated.