Engineering Analysis/Cayley Hamilton Theorem

If the characteristic equation of matrix A is given by:


 * $$\Delta(\lambda) = |A-\lambda I| = (-1)^n(\lambda^n + a_{n-1}\lambda^{n-1} + \cdots + a_0) = 0$$

Then the Cayley-Hamilton theorem states that the matrix A itself is also a valid solution to that equation:


 * $$\Delta(A) = (-1)^n(A^n + a_{n-1}A^{n-1} + \cdots + a_0) = 0$$

Another theorem worth mentioning here (and by "worth mentioning", we really mean "fundamental for some later topics") is stated as: