An eigenvector is a nonzero vector who's direction is unchanged (or reversed) by a linear map. The quantity that an eigenvector is scaled by under the mapping is called the eigenvalue and is written as a . Eigenvectors only exist for square matrices as for others they would either be all vectors or .

Formally given a linear map which is a square matrix the vector and the scalar are an eigenvector and eigenvalue of if the following equation holds true: