- #1

- 116

- 0

## Homework Statement

Suppose that N is a nilpotent mxm matrix, N[itex]^{m}[/itex]=0, but N[itex]^{m'}[/itex][itex]\neq[/itex]0 for m'<m. Show that there exists a basis in which it takes the form of a single Jordan block with vanishing diagonal elements. Prove that your basis set is linearly independent.

## Homework Equations

## The Attempt at a Solution

So I've recognized the fact that N[itex]^{m'}[/itex][itex]\neq[/itex]0 for m'<m means that N[itex]^{m'}[/itex] does not annihilate every vector in V. I'm just not really sure where go from here...