Question

Find the jordan canonical form of a 6*6 matrix

Answer 1

Well, if Nl and N2 are 6 X 6 nilpotent matrices, the characteristic polynomial of them, are p1(x)=p2(x)=x^6 and the minimal m1(x)=m2(x)=x^i with i=1,...,6. As these matrices has same nullity, (call it "s") then rank(N1)=rank(N2)=6-s.