A nilpotent element of a ring has $a^n=0$ for some integer $n$.
A nilpotent element of a ring has $a^n=0$ for some integer $n$.
For example, in the ring $\mathbb{M_{2\times2}}$, $\begin{pmatrix}0&1\\0&0\end{pmatrix}$ is nilpotent with degree $2$.
Questions tagged [nilpotence]
613 questions
0
votes
2 answers
True or false? If two matrices $A,B$ are nilpotent and have the same Jordan normal form, $A+B$ is also nilpotent.
I do know that $(n \times n)$ nilpotent matrices have the minimal polynomial $x^k$ for some positive integer $k ≤ n$.
I also do know that having the same Jordan normal form means they have the same minimal polynomial.
Any hints are welcome, I…
B.Swan
- 2,469