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