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## Homework Statement

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; J

_{n}(2)\...\J

_{n}(-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.