- #1

glacier302

- 35

- 0

## Homework Statement

If the characteristic polynomial of an operator T is (-1)^n*t^n, is T nilpotent?

## Homework Equations

## The Attempt at a Solution

My first instinct for this question is that the answer is yes, because the matrix form of T must have 0's on the diagonal and must be either upper triangular or lower triangular. This is what I found when I tried to find 2x2 and 3x3 matrices with characteristic polynomial (-1)^n*t^n. However, I'm not sure how to actually prove this fact (especially for the nxn case), or how to show that T is nilpotent using this fact.

Any help would be much appreciated : )