On trace zero symplectic matrices

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-06-18 DOI:10.1016/j.laa.2025.06.011

Ralph John L. de la Cruz, Kae Mark T. Domingo

引用次数: 0

Abstract

It is known that every 2n-by-2n complex matrix A is a sum of three symplectic matrices. We show that if A has zero trace, then the summands may be taken to have zero trace as well. We prove an analogous result for real matrices. We also characterize 2-by-2 real matrices that can be written as a sum of two trace zero symplectic matrices.

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跟踪零辛矩阵

已知每个2n × 2n的复矩阵A是三个辛矩阵的和。我们证明如果A有零迹，那么求和也可以取为零迹。我们证明了实矩阵的一个类似结果。我们也描述了2 × 2实矩阵，它可以写成两个迹零辛矩阵的和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.