What does it mean to say that a matrix can be diagonalised? Given that the real matrix has eigenvectors satisfying , explain how to obtain the diagonal form of . Prove that is indeed diagonal. Obtain, with proof, an expression for the trace of in terms of its eigenvalues.
The elements of are given by
Determine the elements of and hence show that, if is an eigenvalue of , then
Assuming that can be diagonalised, give its diagonal form.