Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras

Dimiter Prodanov

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arXiv · 2308.02291

Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras

Dimiter Prodanov

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Abstract

The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into non-commutative multivectors. The paper demonstrates an algorithm for the computation of inverses of such numbers in a non-degenerate Clifford algebra of an arbitrary dimension. The algorithm is a variation of the Faddeev-LeVerrier-Souriau algorithm and is implemented in the open-source Computer Algebra System Maxima. Symbolic and numerical examples in different Clifford algebras are presented.

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Dimiter Prodanov. 2023-08-04. Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras. https://arxiv.org/abs/2308.02291

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