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Multivector and multivector matrix inverses in real Clifford algebras

Hitzer, Eckhard and Sangwine, Stephen (2017) 'Multivector and multivector matrix inverses in real Clifford algebras.' Applied Mathematics and Computation, 311. pp. 375-389. ISSN 0096-3003

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We show how to compute the inverse of multivectors in finite dimensional real Clifford algebras Cl(p, q). For algebras over vector spaces of fewer than six dimensions, we provide explicit formulae for discriminating between divisors of zero and invertible multivectors, and for the computation of the inverse of a general invertible multivector. For algebras over vector spaces of dimension six or higher, we use isomorphisms between algebras, and between multivectors and matrix representations with multivector elements in Clifford algebras of lower dimension. Towards this end we provide explicit details of how to compute several forms of isomorphism that are essential to invert multivectors in arbitrarily chosen algebras. We also discuss briefly the computation of the inverses of matrices of multivectors by adapting an existing textbook algorithm for matrices to the multivector setting, using the previous results to compute the required inverses of individual multivectors.

Item Type: Article
Uncontrolled Keywords: Clifford algebra; Inverse; Multivector matrix algebra
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Science and Health
Faculty of Science and Health > Computer Science and Electronic Engineering, School of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 13 Jun 2017 10:36
Last Modified: 06 Jan 2022 14:47

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