Intuition Behind The Cayley Hamilton Theorem

We try to gain an intuitive understanding for the Cayley Hamilton theorem. Working in the 2x2 case only, we do this by considering properties of eigenvalues and eigenvalues. 00:00 Characteristic equation 01:30 Eigenvalues & eigenvectors 03:53 Linear combinations 05:39 Main argument 08:58 No real eigenvalues 12:51 Repeated eigenvalues: sufficient condition 16:32 Repeated eigenvalues: proof