Home /
Expert Answers /
Advanced Math /
7-in-the-jordan-normal-form-theorem-give-a-dimension-counting-argument-to-show-that-the-number-o-pa782
(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 Jordan block is independent of the decomposition.
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