# Nilpotent Operator

1. Apr 3, 2006

Suppose V is finite dimensional and N:V->V is a linear transformation such that N^e=0. Is it possible to show that e$$\leq$$dim V? Is it even true?

2. Apr 3, 2006

### matt grime

Yes, it is very easy to show this, or rather the correct statement when e is the minimal positive integer such that N^e=0, so try it.

3. Apr 3, 2006