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If $v$ is a vector that is not the zero vector, then it is an eigenvector of a linear transformation $T$ if $T(v)$ is a scalar multiple of $v$. This condition can be written as the equation

$$ T(\mathbf{v}) = \lambda \mathbf{v},$$

where $λ$ is a scalar known as the eigenvalue or characteristic value associated with the eigenvector $v$