Hey guys, I have a question here that reads:
Suppose that N belongs to L(V) is such that nullN^dimV does not equal nullN^dimv-1. Prove that N is nillpotent and dim nullN^j = j for 0 is less than or equal to j which is less than or equal to dimV. What is the Jordan form and Jordan basis of T?
I am very frusterated and confused with this question as I havent the slightest idea on how to tackle it. Could anyone give me any bit of guidance towards solving this question? Thanks a lot guys, appreciate any and all help.