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Published on Apr 22, 2015
I yet again go through the set-up for the nilpotent map's cannonical form as built from the k-cycles. We also used the tableau to organize our thinking about the all the cycles for a given nilpotent map. This then is used to see where the Jordan blocks come from. Each Jordan block stems from looking at T-lambda*I restricted to K_i the i-th generalized e-space. I called this restricted map N_i and as it is nilpotent we are able to find a basis for K_i which places N_i in cannonical form. This leads to the Jordan form. I do not prove the central result, I encourage those interested to see the text for proof. Finally, I mention three major applications of the Jordan form. These are just the tip of the iceberg, next time: minimal polynomials and homework help.