Eigenvalue

In linear algebra an eigenvalue of a (square) matrix $A$ is a number $\lambda$ that satisfies the eigenvalue equation,

${\text{det}}(A-\lambda I)=0\ ,$

where $I$ is the identity matrix of the same dimension as $A$ and in general $\lambda$ can be complex. The origin of this equation is the eigenvalue problem, which is to find the eigenvalues and associated eigenvectors of $A$. That is, to find a number $\lambda$ and a vector ${\vec {v}}$ that together satisfy

$A{\vec {v}}=\lambda {\vec {v}}\ .$