Eigenvalues and Eigenvectors

An eigenvector is a non-zero vector such that when a linear transformation is applied, does not change its direction. The corresponding eigenvalue is the factor of which the eigenvector is scaled.

Solving

• An eigenvector can be found by solving $|A=\lambda I|=0$
• An eigenvalue of a system is: $\det (A-\lambda I)=0$

These eigenvalues are stable if $\mathrm{Re}(\lambda )<0$.