Characteristic Polynomial

polynomial p(λ)=α0λn+α1λn1+...+αn1λ1+αnp(\lambda)=\alpha_0\lambda^n+\alpha_1\lambda^{n-1}+...+\alpha_{n-1}\lambda^{1}+\alpha_n

p(λ)=det(AλI)\begin{gather*} p(\lambda)=det(A-\lambda I) \end{gather*}

Solving

p(λ)=0\begin{gather*} p(\lambda)=0 \end{gather*}

Gives λ\lambda values which are eigenvalues of A