Hitzer, Eckhard and Sangwine, Stephen (2019) Construction of multivector inverse for Clifford algebras over 2m+1-dimensional vector spaces from multivector inverse for Clifford algebras over 2m-dimensional vector spaces. Advances in Applied Clifford Algebras, 29 (2). DOI https://doi.org/10.1007/s00006-019-0942-7
Hitzer, Eckhard and Sangwine, Stephen (2019) Construction of multivector inverse for Clifford algebras over 2m+1-dimensional vector spaces from multivector inverse for Clifford algebras over 2m-dimensional vector spaces. Advances in Applied Clifford Algebras, 29 (2). DOI https://doi.org/10.1007/s00006-019-0942-7
Hitzer, Eckhard and Sangwine, Stephen (2019) Construction of multivector inverse for Clifford algebras over 2m+1-dimensional vector spaces from multivector inverse for Clifford algebras over 2m-dimensional vector spaces. Advances in Applied Clifford Algebras, 29 (2). DOI https://doi.org/10.1007/s00006-019-0942-7
Abstract
Assuming known algebraic expressions for multivector inverses in any Clifford algebra over an even dimensional vector space Rp′,q′, n ′ = p ′ + q ′ = 2 m, we derive a closed algebraic expression for the multivector inverse over vector spaces one dimension higher, namely over R p,q , n= p+ q= p ′ + q ′ + 1 = 2 m+ 1. Explicit examples are provided for dimensions n ′ = 2 , 4 , 6 , and the resulting inverses for n= n ′ + 1 = 3 , 5 , 7. The general result for n= 7 appears to be the first ever reported closed algebraic expression for a multivector inverse in Clifford algebras Cl(p, q), n= p+ q= 7 , only involving a single addition of multivector products in forming the determinant.
Item Type: | Article |
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Uncontrolled Keywords: | Clifford algebra; Multivector determinants; Multivector inverse |
Subjects: | Q Science > QA Mathematics |
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: | 18 Mar 2019 14:34 |
Last Modified: | 30 Oct 2024 16:27 |
URI: | http://repository.essex.ac.uk/id/eprint/24033 |
Available files
Filename: 1901.0246v1.pdf