Simultaneous Diagonalization Under Weak Regularity and a Characterization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-09-17 DOI:10.1007/s10957-024-02526-y

Fabián Flores-Bazán, Felipe Opazo

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Abstract

We analyze the fulfillment of the simultaneous diagonalization (SD via congruence) property for any two real matrices, and develop sufficient conditions expressed in different way to those appeared in the last few years. These conditions are established under a different perspective, and in any case, they supplement and clarify other similar results published elsewhere. Following our point of view reflected in a previous work, we offer some necessary and sufficient conditions, different in nature to those in Jiang and Li (SIAM J Optim 26:1649–1668, 2016), for SD: roughly speaking our approach is more geometric and needs to compute images and kernels of matrices; whereas that in Jiang and Li (SIAM J Optim 26:1649–1668, 2016) requires to compute determinant and canonical forms. The bidimensional situation is particularly analyzed, providing new more precise characterizations than those in higher dimension and joint those given earlier by the authors. In addition, we also establish the connection of our characterization of SD with that provided in Jiang and Li (SIAM J Optim 26:1649–1668, 2016).

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弱规则性下的同时对角线化及其特征

我们分析了任意两个实数矩阵的同时对角化（通过全等的 SD）性质的实现，并提出了与过去几年中出现的不同的充分条件。这些条件是在不同的视角下建立的，无论如何，它们补充并澄清了其他地方发表的类似结果。根据我们在之前工作中反映的观点，我们为SD提供了一些必要和充分条件，这些条件在性质上不同于Jiang和Li（SIAM J Optim 26:1649-1668，2016）中的条件：粗略地说，我们的方法更加几何化，需要计算矩阵的图像和核；而Jiang和Li（SIAM J Optim 26:1649-1668，2016）中的方法需要计算行列式和典范形式。我们特别分析了二维情况，提供了比高维情况更精确的新表征，并与作者早先给出的表征相结合。此外，我们还建立了 SD 特征描述与 Jiang 和 Li（SIAM J Optim 26:1649-1668, 2016）所提供的特征描述之间的联系。

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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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