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arXiv · 2606.23259

Explicit Formula for Inverse and Determinant in Geometric Algebras over Odd-dimensional Vector Spaces

K. S. Abdulkhaev·D. S. Shirokov
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Abstract

In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension $n=7$. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces from the known even-dimensional case. To validate computational utility of the results, we provide a numerical implementation of the formulas. The code implementation is available at the repository github.com/kamranuz/clifford_7d. These formulas extend previous results for lower dimensions and offer new insights for applications in mathematical physics and computational geometry.

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BibTeXRIS

K. S. Abdulkhaev, D. S. Shirokov. 2026-06-22. Explicit Formula for Inverse and Determinant in Geometric Algebras over Odd-dimensional Vector Spaces. https://arxiv.org/abs/2606.23259

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