# Questions tagged [nilpotent-matrices]

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### Algorithm for the nilpotence of matrix polynomials

Let $P$ be a multivariate polynomial of real-valued $N \times N$ matrices. Given $X_1, X_2, ..., X_M \in \mathcal{M}_N\{\mathbb{R}\}$, is there any optimal algorithm to determine whether the result of ...
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### cohomology of nilpotent matrices of fixed $m$-th power

Let $k$ be an algebraically closed field, $\mathcal{N}$ is the variety of $n \times n$ nilpotent matrices over $k$, and consider the natural $m$-power map $\mathcal{N} \rightarrow \mathcal{N}$ given ...
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### Request for info on the space of commuting matrices preserving a flag.

Fix a flag of subspaces V1 in V2 in V3, etc. all in Cn. Consider the space of pairs of commuting linear transformations A and B such that: A preserves the flag (i.e. A(Vi) is in Vi), and B strictly ...
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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 ...
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 $\ker AB = ... 3answers 636 views ### Conjugacy class of a full Jordan block over integers Can we characterize all integer matrices that are similar (over$\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}...