{"paper":{"title":"Euclidean Clifford Algebra","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. M. Moya, V. V. Fern\\'andez, W. A. Rodrigues Jr","submitted_at":"2002-12-13T17:25:34Z","abstract_excerpt":"Let $V$ be a $n$-dimensional real vector space. In this paper we introduce the concept of \\emph{euclidean} Clifford algebra $\\mathcal{C\\ell}(V,G_{E})$ for a given euclidean structure on $V,$ i.e., a pair $(V,G_{E})$ where $G_{E}$ is a euclidean metric for $V$ (also called an euclidean scalar product). Our construction of $\\mathcal{C\\ell}(V,G_{E})$ has been designed to produce a powerful computational tool. We start introducing the concept of \\emph{multivectors} over $V.$ These objects are elements of a linear space over the real field, denoted by $\\bigwedge V.$ We introduce moreover, the conce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212043","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}