Geometric Algebra for Subspace Operations

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dc.creatorBouma, T. A.
dc.creatorDorst, L.
dc.creatorPijls, H. G. J.
dc.date2001-04-09
dc.date.accessioned2026-07-07T04:41:14Z
dc.date.available2026-07-07T04:41:14Z
dc.descriptionThe set theory relations \in, \backslash, Δ, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and Δare easily subsumed by Geometric Algebra for Euclidean metrics. A short computation shows that the meet (\cap) and join (\cup) are resolved in a projection operator representation with the aid of one additional product beyond the standard Geometric Algebra products. The result is that the join can be computed even when the subspaces have a common factor, and the meet can be computed without knowing the join. All of the operations can be defined and computed in any signature (including degenerate signatures) by transforming the problem to an analogous problem in a different algebra through a transformation induced by a linear invertible function (a LIFT to a different algebra). The new results, as well as the techniques by which we reach them, add to the tools available for subspace computations.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0104102
dc.identifierhttp://arxiv.org/abs/math/0104102
dc.identifierActa Applicandae Mathematicae 73(3): 285--300, 2002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61272
dc.subjectRings and Algebras
dc.subjectMetric Geometry
dc.subject06-XX, 08-XX, 15-XX, 15A66, 51-XX
dc.titleGeometric Algebra for Subspace Operations
dc.typetext

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