Construction of 4 x 4 symmetric stochastic matrices with given spectra

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-16 DOI:10.1515/math-2023-0176

Jaewon Jung, Donggyun Kim

引用次数: 0

Abstract

The symmetric stochastic inverse eigenvalue problem (SSIEP) asks which lists of real numbers occur as the spectra of symmetric stochastic matrices. When the cardinality of a list is 4, Kaddoura and Mourad provided a sufficient condition for SSIEP by a mapping and convexity technique. They also conjectured that the sufficient condition is the necessary condition. This study presents the same sufficient condition for SSIEP, but we do it in terms of the list elements. In this way, we provide a different but more straightforward construction of symmetric stochastic matrices for SSIEP compared to those of Kaddoura and Mourad.

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构建具有给定频谱的 4 x 4 对称随机矩阵

对称随机逆特征值问题（SSIEP）询问哪些实数列表会出现在对称随机矩阵的谱中。当列表的卡片数为 4 时，Kaddoura 和 Mourad 通过映射和凸性技术为 SSIEP 提供了充分条件。他们还猜想，充分条件就是必要条件。本研究为 SSIEP 提出了同样的充分条件，但我们是从列表元素的角度提出的。这样，与 Kaddoura 和 Mourad 的研究相比，我们为 SSIEP 提供了一种不同但更直接的对称随机矩阵构造。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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