The quadratic sum problem for symplectic pairs

被引:0
|
作者
Pazzis, Clement de Seguins [1 ]
机构
[1] Univ Versailles St Quentin En Yvelines, Lab Math Versailles, 45 Ave Etats Unis, F-78035 Versailles, France
关键词
Symplectic forms; Invariant factors; Quadratic elements; Decomposition; MATRICES; PRODUCTS;
D O I
10.1016/j.laa.2023.12.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let (b, u) be a pair consisting of a symplectic form b on a finite-dimensional vector space V over a field F, and of a b -alternating endomorphism u of V (i.e. b(x, u(x)) = 0 for all x in V ). Let p and q be arbitrary polynomials of degree 2 with coefficients in F. We characterize, in terms of the invariant factors of u, the condition that u splits into u1 + u2 for some pair (u1, u2) of b-alternating endomorphisms such that p(u1) = q(u2) = 0. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码:151 / 179
页数:29
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