Multivector Contractions Revisited, Part I

TL;DR

This paper revisits and extends the theory of multivector contractions, providing new results, generalizations, and clarifications, especially relating to geometric algebra and duality concepts.

Contribution

It reorganizes and simplifies the theory of multivector contractions, introduces new formulas, and compares different conventions, enhancing understanding and application of geometric algebra.

Findings

New geometric characterizations of blade contractions

Higher-order graded Leibniz rules derived

Improved complex star operators introduced

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.