Be A an M_6(R) matrix so that A^4-8A^2 +16I = 0. What are the possible Jordan Forms non similar to A?
I tried to solve that, so I arrived in the equation (A-2I)^2*(A+2I)^2 = 0. So this will give me two possibilies of characteristic equation: (x-2)^4*(x+2)^2 = 0 or (x-2)^2*(x+2)^4 = 0. So to the case 1: eigenvalue 2 I can have: 2 jordan blocks of size two, or one jordan block of size two and two jordan blocks of size one eigenvalue -2 I can have: 2 jordan blocks of size one
Case 2. The same thing but switching the eigenvalues.
Am I right?