Definition of eigenvalue of a matrix
Definition: A scalar $\lambda$ is an eigenvalue of an $n \times n$ matrix $A$ if there exists a nonzero vector $v$ such that $Av = \lambda v$. Equivalently, $\det(A - \lambda I) = 0$.
Definition: A scalar $\lambda$ is an eigenvalue of an $n \times n$ matrix $A$ if there exists a nonzero vector $v$ such that $Av = \lambda v$. Equivalently, $\det(A - \lambda I) = 0$.