Zobrazeno 1 - 10
of 1 077
pro vyhledávání: '"15A21"'
Publikováno v:
Linear and Multilinear Algebra vol 67, issue 5 (2019), pages 939-952
Let $\mathbb{F}$ be a field of characteristic $\neq 2$ and $3$, let $V$ be a $\mathbb{F}$-vector space of dimension $6$, and let $\Omega \in \wedge ^2V^\ast $ be a non-degenerate form. A system of generators for polynomial invariant functions under t
Externí odkaz:
http://arxiv.org/abs/2412.03135
Autor:
Lohan, Tejbir, Maity, Chandan
We consider the adjoint action of the symplectic Lie group $\mathrm{Sp}(2n,\mathbb{C})$ on its Lie algebra $\mathfrak{sp}(2n,\mathbb{C})$. An element $X \in \mathfrak{sp}(2n,\mathbb{C})$ is called $\mathrm{Ad}_{\mathrm{Sp}(2n,\mathbb{C})}$-real if $
Externí odkaz:
http://arxiv.org/abs/2411.09575
Positive spanning sets (PSSs) are families of vectors that span a given linear space through non-negative linear combinations. Despite certain classes of PSSs being well understood, a complete characterization of PSSs remains elusive. In this paper,
Externí odkaz:
http://arxiv.org/abs/2411.08994
Autor:
Sergeraert, Francis
The Smith reduction is a basic tool when analyzing integer matrices up to equivalence, and the Kannan-Bachem (KB) algorithm is the first polynomial algorithm computing such a reduction. Using this algorithm in complicated situations where the rank of
Externí odkaz:
http://arxiv.org/abs/2411.02422
An element of a group is called reversible if it is conjugate to its own inverse. Reversible elements are closely related to strongly reversible elements, which can be expressed as a product of two involutions. In this paper, we classify the reversib
Externí odkaz:
http://arxiv.org/abs/2410.01587
A commutator of unipotent matrices of index 2 is a matrix of the form $XYX^{-1}Y^{-1}$, where $X$ and $Y$ are unipotent matrices of index 2, that is, $X\ne I_n$, $Y\ne I_n$, and $(X-I_n)^2=(Y-I_n)^2=0_n$. If $n>2$ and $\mathbb F$ is a field with $|\m
Externí odkaz:
http://arxiv.org/abs/2409.13339
Autor:
Vineyard, Jimmy
Let $d$ denote a nonnegative integer and let $\mathbb{F}$ denote a field. Let $V$ denote a $d+1$ dimensional vector space over $\mathbb{F}$. Given an ordering $\{\theta_i\}_{i=0}^d$ of the eigenvalues of a multiplicity-free linear map $A: V \to V$, w
Externí odkaz:
http://arxiv.org/abs/2410.07178
Let $K$ be a field, $R=K[x, y]$ the polynomial ring and $\mathcal{M}(K)$ the set of all pairs of square matrices of the same size over $K.$ Pairs $P_1=(A_1,B_1)$ and $P_2=(A_2,B_2)$ from $\mathcal{M}(K)$ are called similar if $A_2=X^{-1}A_1X$ and $B_
Externí odkaz:
http://arxiv.org/abs/2408.04244
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative examples ar
Externí odkaz:
http://arxiv.org/abs/2407.17995
Rosenbrock's theorem on polynomial system matrices is a classical result in linear systems theory that relates the Smith-McMillan form of a rational matrix $G$ with the Smith forms of an irreducible polynomial system matrix $P$ giving rise to $G$ and
Externí odkaz:
http://arxiv.org/abs/2406.18218