矩阵拉伸

IF 1 4区数学 Q1 MATHEMATICS

Open Mathematics 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。

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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

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: