Connections between matrix products for 3-vectors and geometric algebra

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dc.contributor.authorBongardt, Bertold
dc.contributor.authorLöwe, Harald
dc.coverage.issue1cs
dc.coverage.volume12cs
dc.date.accessioned2023-06-26T09:02:08Z
dc.date.available2023-06-26T09:02:08Z
dc.date.issued2023cs
dc.description.abstractThe geometric product represents a core concept for establishing geometric algebras and in case of vectors matches the formal sum of their inner product and their wedge product. The geometric product is reconsidered for the case of 3-vectors by means of usual matrix algebra in this article. Therefore, a symmetric matrix product and an antisymmetric matrix product are introduced, whose matrix sum yields a third product that renders the information of a vector pair’s geometric product in terms of a matrix associated to the vectors. The three matrices – that correspond to inner product, wedge product, and geometric product, respectively – are named wheel product, curl product, and full product. The observation about the structural correspondence of the geometric product with matrix theory may be used for future practical computations and unveils connections of geometric algebra with related disciplines.en
dc.formattextcs
dc.format.extent1-25cs
dc.format.mimetypeapplication/pdfen
dc.identifier.citationMathematics for Applications. 2023 vol. 12, č. 1, s. 1-25. ISSN 1805-3629cs
dc.identifier.doi10.13164/ma.2023.01en
dc.identifier.issn1805-3629
dc.identifier.urihttp://hdl.handle.net/11012/210630
dc.language.isoencs
dc.publisherVysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.relation.ispartofMathematics for Applicationsen
dc.relation.urihttp://ma.fme.vutbr.cz/archiv/12_1/ma_12_1_bongart_lowe_final.pdfcs
dc.rights© Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematikycs
dc.rights.accessopenAccessen
dc.subjectgeometric algebraen
dc.subjectlinear algebraen
dc.subjectline geometryen
dc.subjectLie–Jordan productsen
dc.titleConnections between matrix products for 3-vectors and geometric algebraen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
eprints.affiliatedInstitution.departmentÚstav matematikycs
eprints.affiliatedInstitution.facultyFakulta strojního inženýrstvícs
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