Engineering Analysis/Cayley Hamilton Theorem

If the characteristic equation of matrix A is given by: Then the Cayley-Hamilton theorem states that the matrix A itself is also a valid solution to that equation: Another theorem worth mentioning here (and by "worth mentioning", we really mean "fundamental for some later topics") is stated as: If λ are the eigenvalues of matrix A, and if there is a function f that is defined as a linear combination of powers of λ: If this function has a radius of convergence S, and if all the eigenvectors of A have magnitudes less than S, then the matrix A itself is also a solution to that function: