Multivector Contractions Revisited, Part I
Abstract
We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new ones are given, like: geometric characterizations of blade contractions and regressive products, higher-order graded Leibniz rules, determinant formulas, improved complex star operators, etc. Different contractions and conventions found in the literature are discussed and compared, in special those of Clifford Geometric Algebra. Applications of the theory are developed in a follow-up paper.
Cite
@article{arxiv.2205.07608,
title = {Multivector Contractions Revisited, Part I},
author = {André L. G. Mandolesi},
journal= {arXiv preprint arXiv:2205.07608},
year = {2024}
}
Comments
The manuscript has been reformulated, and divided in two: this one, with the basic theory of contractions and star duality, and arXiv:2401.11299 with applications. Some results have been simplified, new ones included, and others removed for the sake of space