divx

Oh okay that makes sense, thank you

But a polynomial of degree n doesn't necessarily have n real solutions

Yes of course

It doesn't specify, but probably

How come?

Ohh... I forgot about the complex eigenvalues, thank you

@LeakyNun so a 4x4 matrix always has 4 solutions to the characteristic equation (even if these solutions can be the same)?

Can someone explain why a 4x4 rank 1 matrix with an eigenvalue of 0 multiplicity 3, has to be diagonalizable? I understand that rank 1 would mean that the dimension of the Eigenspace(0) is 3 but where does the other eigenvalue come from?