有界秩矩阵空间上的Schur定理与dieudonn定理的联系

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-05-07 DOI:10.1016/j.laa.2025.05.001

Clément de Seguins Pazzis

引用次数: 0

摘要

利用双对偶论证给出了奇异矩阵空间上diudonn定理的一个新的证明。该论证将这种情况与秩最多为1的算子的空间结构联系起来，并且在代数闭域上效果最好。

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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A connection between Schur and Dieudonné's theorems on spaces of bounded rank matrices

We use a double-duality argument to give a new proof of Dieudonné's theorem on spaces of singular matrices. The argument connects the situation to the structure of spaces of operators with rank at most 1, and works best over algebraically closed fields.

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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.