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(Solved): 7. In the Jordan Normal Form theorem, give a dimension counting argument to show that the number o ...



7. In the Jordan Normal Form theorem, give a dimension counting argument to show that
the number of factors with a given Jord

7. In the Jordan Normal Form theorem, give a dimension counting argument to show that the number of factors with a given Jordan block is independent of the decomposition.


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Step 1. Find all Jordan blocks J = J(?, m) satisfying J 2 = I. By the explicit formula of powers of Jordan blocks , this can only happen if m = 1. Furthermore, in that c
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