Let A be an n×n matrix whose characteristic polynomial splits, γ be a cycle of generalized eigenvectors corresponding to an eigenvalue λ, and W be the subspace spanned by γ. Define γ’ to be the ordered set obtained from γ by reversing the order of the vectors in γ. (a) Prove that [TW]γ’ = ([TW]γ)t. (b)Let J be the Jordan canonical form of A. Use (a) to prove that J and Jt are similar. (c) Use (b) to prove that A and At are similar.

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