Affiliation:
1. Department of Mathematics, Faculty of Economic Sciences HSE University Moscow 101000 Russia
2. Laboratory 1 Institute for Information Transmission Problems of the Russian Academy of Sciences Moscow 127051 Russia
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 formulas with the ordinary Vieta 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. We introduce the notion of a simple basis‐free formula for a determinant in geometric algebra and prove that a formula of this type exists in the case of arbitrary dimension. Using this notion, we present and prove generalized Vieta theorem in geometric algebra of arbitrary dimension. The results can be used in symbolic computation and various applications of geometric algebras in computer science, computer graphics, computer vision, physics, and engineering.
Subject
General Engineering,General Mathematics
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