# Questions tagged [nilpotent-matrices]

The tag has no usage guidance.

14 questions
Filter by
Sorted by
Tagged with
322 views

Let $\boldsymbol{V}_{1},\dots,\boldsymbol{V}_{n}\in\mathbb{R}^{d\times m}$ be $n$ “tall” matrices (where $d\ge m$) with orthonormal columns. And let $\boldsymbol{P}_{1},\dots,\boldsymbol{P}_{n}\in\... 2 votes 0 answers 208 views ### For a nilpotent matrix A, are the cardinalities of sets: 1) B: commute with A, 2) B: anticommute with A, 3) B: q-commute with A — the same? Let us work over finite fields$F_{p^k}$. Simulations seems to indicate: Question 1: Consider a nilpotent matrix$A$, consider the set of all matrices$B$, such that$AB-qBA=0$, then cardinality of ... 1 vote 0 answers 105 views ### Algorithm for the nilpotence of matrix polynomials Let$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}\}$, is there any optimal algorithm to determine whether the result of ... 3 votes 0 answers 97 views ### cohomology of nilpotent matrices of fixed$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}$given ... 2 votes 2 answers 745 views ### Simultaneous upper-triangularization for two nilpotent commuting matrix Given two nilpotent matrix B1 and B2 over complex numbers which commute i.e. [B1,B2]=0, we know that they can be conjugated to upper-triangular ones (even strictly-triangular since they're nilpotent). ... 0 votes 1 answer 103 views ### About indecomposability and nilpotence Transferred from MSE where it now received a complete answer. Maybe the following is easy, but I am not an expert in finite-dimensional Lie algebras and was stuck on the following problem. Can ... 2 votes 1 answer 311 views ### Commuting nilpotent matrix collection For every large enough$m\in\Bbb N$are there$c=\alpha m$(for some fixed$\alpha>0$) square matrices$A_1,\dots,A_c$that commute with each other with nonzero product ($\forall i,j\in\{1,\dots,t\}... 766 views