On SVD and Polar Decomposition in Real and Complexified Clifford Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-27 DOI:10.1007/s00006-024-01328-9

Dmitry Shirokov

引用次数: 0

Abstract

In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified Clifford geometric algebras of arbitrary dimension and signature. The new theorems involve only operations in geometric algebras and do not involve matrix operations. We naturally define these and other related structures such as Hermitian conjugation, Euclidean space, and Lie groups in geometric algebras. The results can be used in various applications of geometric algebras in computer science, engineering, and physics.

查看原文本刊更多论文

论实数和复数克利福德代数中的 SVD 和极性分解

在本文中，我们提出了在任意维数和签名的非enerate实数和复数化克利福德几何代数中对任意多向量进行奇异值分解（SVD）和极性分解的自然实现方法。新定理只涉及几何代数的运算，不涉及矩阵运算。我们自然而然地定义了几何代数中的这些结构和其他相关结构，如赫尔墨斯共轭、欧氏空间和李群。这些结果可用于几何代数在计算机科学、工程学和物理学中的各种应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.