I have a question about nilpotent endomorphism.
Suppose you have an endomorphism $N:V \rightarrow V$ which is nilpotent, such that the degree of nilpotency is equal to the dimension of $V$, i.e. $\dim V = \deg N$. Then the matrix which represents this nilpotent with ordered basis $v, Nv, N^2v .... N^{n-1}v$ is Jordan form of matrix. Actually that is a way of creating Jordan matrix for this endomorphism. My question is how to create this matrix when $\dim V$ is different from $\deg N$?