On Singular Value Decomposition and Polar Decomposition in Geometric Algebras

被引：2
作者：
Shirokov, Dmitry [1 ,2 ]
机构：
[1] HSE Univ, Moscow 101000, Russia
[2] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow 127051, Russia
来源：
ADVANCES IN COMPUTER GRAPHICS, CGI 2023, PT IV | 2024年 / 14498卷
基金：
俄罗斯科学基金会;
关键词：
Clifford algebra; geometric algebra; orthogonal group; polar decomposition; singular value decomposition; SVD; symplectic group; unitary group; LIE-GROUPS;
D O I：
10.1007/978-3-031-50078-7_31
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper is a brief note on the natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real (Clifford) geometric algebras of arbitrary dimension and signature. We naturally define these and other related structures (operation of Hermitian conjugation, Euclidean space, and Lie groups) in geometric algebras. The results can be used in various applications of geometric algebras in computer graphics, computer vision, data analysis, computer science, engineering, physics, big data, machine learning, etc.
引用
收藏
页码：391 / 401
页数：11
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