The Cayley–Hamilton and Frobenius theorems via the Laplace transform

The Cayley–Hamilton theorem on the characteristic polynomial of a matrix A and Frobenius’ theorem on minimal polynomial of A are deduced from the familiar Laplace transform formula . This formula is extended to a formal power series ring over an algebraically closed field of characteristic 0, so that the argument applies in the more general setting of matrices over a field of characteristic 0.