Non-Archimedean Views on Gershgorin’s Theorem and Diagonal Dominance

IF 0.4 4区数学 Q4 MATHEMATICS

American Mathematical Monthly Pub Date : 2023-01-11 DOI:10.1080/00029890.2022.2153558

B. Nica, Dacota Sprague

引用次数: 0

Abstract

Abstract Classical matrix theory works over the complex numbers; its reliance on the usual absolute value makes it an Archimedean theory. In this paper, we consider non-Archimedean counterparts of the Gershgorin disk theorem and diagonally dominant matrices. We compare and contrast the Archimedean and non-Archimedean contexts. A remarkable dissimilarity is that diagonally dominant matrices enjoy more structure in the non-Archimedean setting.

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Gershgorin定理与对角优势的非阿基米德观点

经典矩阵理论适用于复数;它对通常绝对值的依赖使它成为阿基米德理论。本文考虑了Gershgorin盘定理和对角占优矩阵的非阿基米德对偶。我们比较和对比阿基米德和非阿基米德的背景。一个显著的不同是，对角占优矩阵在非阿基米德设置中享有更多的结构。

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

American Mathematical Monthly Mathematics-General Mathematics

CiteScore

0.80

自引率

20.00%

发文量

127

审稿时长

6-12 weeks

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