1. ## Proving nillpotence

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.

2. Originally Posted by GreenDay14
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.

Pleas try to be EXAGGERATEDLY clear with your formulae: from what I can understand you wrote that "Suppose that N belongs to L(V) is such that nullN^dimV does not equal nullN^dimv-1" , or in LaTex:

Suppose $\displaystyle N\in L(V)$ is s.t. $\displaystyle Null(N)\cap dim(V)\neq Null(N)\cap dim(V)-1$

Doesn't make much sense, does it? Please write again what you meant.

Tonio

3. Sorry that I was unclear, but through my mathematics career, ^ has been a general way of expressing -to the power of-, so I was trying to say nullN to the power of dimV, and so on. Sorry again that I was unclear but I hope I make more sense.