In linear algebra, an eigenvector or characteristic vector of a square matrix is a vector that does not change its direction under the associated linear transformation. In other words—if v is a vector that is not zero, then it is an eigenvector of a square matrix A if Av' is a scalar multiple of v. This condition could be written as the equation:

where λ is a scalar known as the eigenvalue or characteristic value associated with the eigenvector v. Geometrically, an eigenvector corresponding to a real, nonzero eigenvalue points in a direction that 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.