Take a look at this theorem. Is it a way to show this theorem? I would like to show it using the standard way of diagonalizing a matrix. I mean if P = [v1 v2] and D = [lambda1 0 0 lambda D] We have that AP = PD even for complex eigenvectors and eigenvalues. But the P matrix in this theorem is real, and so is the C matrix. I think they have used that v1 and v2 are conjugates, and so is lambda 1 and lambda 2. How would you show this theorem? Can you use ordinary diagonolisation to show it?