On noncommutative Vieta theorem in geometric algebras

DOI10.1007/978-3-031-30923-6_3zbMath1520.15008arXiv2301.06848OpenAlexW4367147840MaRDI QIDQ6134239

Dmitry Shirokov

Publication date: 21 August 2023

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.06848

zbMATH Keywords

characteristic polynomialClifford algebrageometric algebraVieta's formulasnoncommutative Vieta theoremVieta theorem

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Clifford algebras, spinors (15A66) Applications of Clifford algebras to physics, etc. (15A67)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Clifford algebra to geometric calculus. A unified language for mathematics and physics
• Quasideterminants. I
• Matrix Vieta theorem revisited
• The inverse of a multivector: beyond the threshold \(p+q=5\)
• Multivector and multivector matrix inverses in real Clifford algebras
• Noncommutative symmetric functions
• Basis-free formulas for characteristic polynomial coefficients in geometric algebras
• Basis-free solution to Sylvester equation in Clifford algebra of arbitrary dimension
• On computing the determinant, other characteristic polynomial coefficients, and inverse in Clifford algebras of arbitrary dimension
• Concepts of trace, determinant and inverse of Clifford algebra elements

This page was built for publication: On noncommutative Vieta theorem in geometric algebras