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--- geometric_algebra [2020/07/10 17:12] – [Articles] pbk
+++ geometric_algebra [2020/07/19 16:33] – [Wikipedia links] pbk
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   * [[https://en.wikipedia.org/wiki/Multivector|Multivector]]
   * [[https://en.wikipedia.org/wiki/Paravector|Paravector]]
+  * [[https://en.wikipedia.org/wiki/Outermorphism|Outermorphism]]
   * [[https://en.wikipedia.org/wiki/Projective_geometry|Projective Geometry]]
   * [[https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates|Plücker coordinates]]
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   * [[https://arxiv.org/pdf/2002.05993|Projective Geometric Algebra as a Subalgebra of Conformal Geometric Algebra]] (2020) - //Jaroslav Hrdina, Ales Navrat, Petr Vasik, Dietmar Hildenbrand//
 First we introduce briefly the frameworks of CGA and PGA for doing Euclidean geometry and we summarise basic formulas. In the next section, we show that there are actually two naturally related copies of PGA in CGA. After an identification of the two copies, the duality in PGA is obtained in terms of CGA operations. This implies directly the correspondence between flat objects and versors for Euclidean transformations in CGA and the objects and versors in PGA.
+  * [[https://link.springer.com/content/pdf/10.1007/s00006-020-1046-0.pdf|A 1d Up Approach to Conformal Geometric Algebra]] (2020) - //Anthony N. Lasenby//
+We discuss an alternative approach to the conformal geometric algebra (CGA) in which just a single extra dimension is necessary, as compared to the two normally used. This is made possible by working in a constant curvature background space, rather than the usual Euclidean space. A possible benefit, which is explored here, is that it is possible to define cost functions for geometric object matching in computer vision that are fully covariant, in particular invariant under both rotations and translations, unlike the cost functions which have been used in CGA so far. An algorithm is given for application of this method to the problem of matching sets of lines, which replaces the standard matrix singular value decomposition, by computations wholly in Geometric Algebra terms, and which may itself be of interest in more general settings. Secondly, we consider a further perhaps surprising application of the 1d up approach, which is to the context of a recent paper by Joy Christian published by the Royal Society, which has made strong claims about Bell's Theorem in quantum mechanics, and its relation to the sphere S^7 and the exceptional group E_8, and proposed a new associative version of the division algebra normally thought to require the octonians.
   * [[https://arxiv.org/pdf/2004.06655|Dimensional scaffolding of electromagnetism using geometric algebra]] (2020) - //Xabier Prado Orbán, Jorge Mira//