Coordinate-free exponentials of general multivector (MV) in Cl(p,q) algebras for p+q=3

2021/08/03 by A. Acus, Acus, A., A. Dargys +1
Computer Science · Mathematics · #15A66 15A67 #Algebraic and Geometric Analysis #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2108.01371

openalex publication_date 2021/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Closed form expressions in a coordinate-free form in real Clifford geometric algebras (GAs) Cl(0,3), Cl(3,0), Cl(1,2) and Cl(2,1) are found for exponential function when the exponent is the most general multivector (MV). The main difficulty in solving the problem is connected with an entanglement or mixing of vector and bivector components. After disentanglement, the obtained formulas simplify to the well-known Moivre-type trigonometric/hyperbolic function for vector or bivector exponentials. The presented formulas may find wide application in solving GA differential equations, in signal processing, automatic control and robotics.

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