A 20 × 20 matrix C has characteristic polynomial (λ^2 − 4)^10. It is given that ker(C−2I), ker (C − 2I)^2, ker (C −2I)^3 and ker (C −2I)^4 have dimensions 3,6,8,10 respectively. It is given that ker (C + 2I), ker (C +2I)^2, ker (C +2I)^3 and ker (C +2I)^4 have di-
mensions 3,5,7,8 respectively. What can be said about the Jordan form of C?
The Attempt at a Solution
I know the eigenvalues of C are +-2 each w/ a multiplicity of 10. So, the Jordan Forms will be; Jn(2)\...\Jn(-2) for each n=1,2,3,... where n is the algebraic multiplicities.
Any help with Jordan Forms, Algebraic and Geometric Multiplicity will be appreciated.
Thanks in advance.