Kamron Abdulkhaev presented a talk at Empowering Novel Geometric Algebra for Graphics & Engineering workshop at Computer Graphics International 2025
Research Assistant of the Laboratory for Geometric Algebra and Applications Kamron Abdulkhaev presented the results of his research at the workshop Empowering Novel Geometric Algebra for Graphics & Engineering (ENGAGE 2025). The ENGAGE workshop is dedicated to cutting-edge research in geometric algebra and its application in computer graphics, engineering, and other fields. The workshop is organized annually as part of the international conference Computer Graphics International (CGI). This year, the CGI 2025 conference was held at The Hong Kong Polytechnic University, Hong Kong, China, from July 14 to 18.
Workshop website: https://engage-workshop.org/
Conference website: https://www.cgs-network.org/cgi25/
Workshop program: https://easychair.org/smart-program/CGI2025/index.html
Talk: Kamron Abdulkhaev & Dmitry Shirokov, 'Explicit Formula for Inverse and Determinant in Geometric Algebras over Seven-dimensional Vector Spaces', July 14, 2025 (online).
Abstract: In this paper, we present an explicit formula for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n=7. We generalize the concept of conjugation to basis conjugation operations, allowing us to express the determinant formula independently of any specific algebra isomorphism. This construction provides a practical computational tool for determining invertibility and calculating inverses of multivectors in geometric algebras associated with seven-dimensional vector spaces. The resulting formulas extend previous results for lower dimensions and offer new insights for applications in mathematical physics and computational geometry.
The results of the talk will be published in the collection Lecture Notes on Computer Science (Scopus - Q2).
We would like to express our gratitude to the HSE Center for Student Academic Development for supporting Kamron's participation in the ENGAGE workshop!
