im given a matrix H from M_n(C) (the space of nxn matrices above the comples field). and we know that for every a in C, dim(ker(H-aI)^2)<=1. prove that H is diagonizable. obviously if i prove that its characteristic poly exists then bacuase every poly above C can be dissected to linear factors, then also its minimal poly can be dissected to linear factors and thus H is diagonaizable, but how to do it? thanks in advance.