On Noncommutative Vieta Theorem in Geometric Algebras

Dmitry Shirokov

Abstract: In this paper, we discuss a generalization of Vieta theorem (Vieta’s formulas) to the case of Clifford geometric algebras. We compare the generalized Vieta’s formulas with the ordinary Vieta’s formulas for characteristic polynomial containing eigenvalues. We discuss Gelfand – Retakh noncommutative Vieta theorem and use it for the case of geometric algebras of small dimensions. The results can be used in symbolic computation and various applications of geometric algebras in computer science, computer graphics, computer vision, physics, and engineering.