(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

3. 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.

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# Jordan Forms, Algebraic and Geometric Multiplicity

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