Hitzer, E and Sangwine, SJ (2016) Multivector and multivector matrix inverses in real Clifford algebras. UNSPECIFIED. CES-534, University of Essex, Colchester.
Hitzer, E and Sangwine, SJ (2016) Multivector and multivector matrix inverses in real Clifford algebras. UNSPECIFIED. CES-534, University of Essex, Colchester.
Hitzer, E and Sangwine, SJ (2016) Multivector and multivector matrix inverses in real Clifford algebras. UNSPECIFIED. CES-534, University of Essex, Colchester.
Abstract
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: | Monograph (UNSPECIFIED) |
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Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Computer software |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Computer Science and Electronic Engineering, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 22 Jul 2016 08:29 |
Last Modified: | 16 May 2024 18:45 |
URI: | http://repository.essex.ac.uk/id/eprint/17282 |
Available files
Filename: TechReport_CES-534.pdf