Understanding N in Jordan Block Matrix

[Wildcat]

Homework Statement

Let J be any Jordan block, i.e. J =λI + N where N is the matrix whose (i,j) entry is δi,j-1.
PJ(λ) is J's characteristic polynomial. Show that PJ(J)=0.

Homework Equations

The Attempt at a Solution

I don't understand what this part of the question means → N is the matrix whose (i,j) entry is δi,j-1. Can someone explain? Does it mean that for example the (2,2) entry of N would be the (2,1) entry of J which would be 0? Making the diagonal entries of N all =0??

 

[Wildcat]

Homework Statement

Let J be any Jordan block, i.e. J =λI + N where N is the matrix whose (i,j) entry is δi,j-1.
PJ(λ) is J's characteristic polynomial. Show that PJ(J)=0.

Homework Equations

The Attempt at a Solution

I don't understand what this part of the question means → N is the matrix whose (i,j) entry is δi,j-1. Can someone explain? Does it mean that for example the (2,2) entry of N would be the (2,1) entry of J which would be 0? Making the diagonal entries of N all =0??

I don't know how to close threads, but while I was waiting for a reply i figured it out!