In general, det(B) = det(A − λI) is a polynomial function of λ. We refer to the function as the characteristic polynomial of A. For instance, in Example 2, the characteristic polynomial of A is λ2 − 5λ + 6. The eigenvalues of A are precisely the solutions of λ in. det(A − λI) = 0. Lemma 1. An n × n matrix A can have at most n distinct eigenvalues.