Let T be a linear operator on a finite-dimensional vector space whose characteristic
Chapter 7, Problem 10(choose chapter or problem)
Let T be a linear operator on a finite-dimensional vector space whose characteristic polynomial splits, and let A be an eigenvalue of T. (a) Suppose that 7 is a basis for KA consist ing of the union of q disjoint cycles of generalized eigenvectors. Prove that q < dim(EA). (b) Let ft be a Jordan canonical basis for T, and suppose that J = [T]^ has q Jordan blocks with A in the diagonal positions. Prove that q < dim(EA).
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