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### A question on Nilpotent Matrix

Suppose we have a linear matrix space $S\subset M_{n\times n}$, any $M\in S$ is a nilpotent matrix, that is $M^n=0$. Then for any finite subset of $S$, says $A=${$M_1,...,M_k$}, one can define the ...
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Prove/ Disprove: Let $n$ be a positive integer. Let $A$, $B$ be two $n \times n$ square matrices over the complex numbers. If $AB = BA$ and $\ker A = \ker A^2$ and $\ker B = \ker B^2$ then $\ker AB = ... 3answers 571 views ### Conjugacy class of a full Jordan block over integers Can we characterize all integer matrices that are similar (over$\Bbb Z$) to a full Jordan block with$0$'a on the diagonal? In other words, can we determine the conjugacy class of such a matrix over$...
I have a nilpotent lie group $N$ with upper central series $$1 = N_0 \triangleleft N_1 \triangleleft \dots \triangleleft N_k = N$$ which induces the filtration 0 = \mathfrak{n}_0 \subset \mathfrak{n}...