Recall that an eigenvector of a matrix A {\displaystyle \mathbf {A} } with corresponsing eigenvalue λ {\displaystyle \mathbf {\lambda } } is a non-zero vector v {\displaystyle \mathbf {v} } that satisfies A v = λ v . {\displaystyle \mathbf {A} \mathbf {v} =\mathbf {\lambda } \mathbf {v} .}