矩阵拉伸

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-03 DOI:10.1515/math-2024-0031

Vyacheslav Futorny, Mikhail Neklyudov, Kaiming Zhao

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引用次数: 0

摘要

我们考虑了不同大小的正方形矩阵的张量积，并引入了拉伸映射，它可以看作是一种广义的矩阵化。拉伸映射保留了张量积的代数特性，但不一定是注入的。抛开注入性条件，我们就能构造出具有额外对称性的拉伸映射实例。此外，这还会导致张量乘的平均化，并可能用于压缩数据。

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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Matrix stretching

We consider the tensor products of square matrices of different sizes and introduce the stretching maps, which can be viewed as a generalized matricization. Stretching maps conserve algebraic properties of the tensor product, but are not necessarily injective. Dropping the injectivity condition allows us to construct examples of stretching maps with additional symmetry properties. Furthermore, this leads to the averaging of the tensor product and possibly could be used to compress the data.

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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.