Let be linear transformation over field, and let be a polynomial over that field.
Prove that nilpotent iff
Thanks!
Yes, I'm aware this fact.
Check me please...
i) [LaTeX ERROR: Convert failed] nilpotent.
[LaTeX ERROR: Convert failed]
Above, sum of nilpotent operators [LaTeX ERROR: Convert failed] nilpotent.
ii) [LaTeX ERROR: Convert failed]
So, there exist [LaTeX ERROR: Convert failed] , index of nilpotents so that[LaTeX ERROR: Convert failed]