8.16 Eigenvalues and Eigenvectors

The scalars, \(\lambda\), that satisfy the polynomial characteristic equation \(|\mathbf{A}-\lambda\mathbf{I}| = 0\) are called eigenvalues of matrix \(\mathbf{A}\).

If \(\mathbf{e}\) is a non-zero vector such that \[\mathbf{Ae} = \lambda\mathbf{e} \] then \(\mathbf{e}\) is said to be an eigenvector of the matrix \(\mathbf{A}\) associated with the eigenvalue \(\lambda\).