Abstract
When a linear space of vectors is devoid of a metric, many quantities can be introduced: multivectors, pseudo-multivectors and their duals, namely forms and pseudo– forms. In R 3, sixteen types of such quantities exist, and to each of them elementary geometric images can be ascribed by replacing traditional line segments with arrows, related to vectors. The possibility of distinguishing, for instance, vectors and linear forms is very important in theoretical physics, where formalisms are used with non-Euclidean spaces or spaces with variable metrics. This is one reason why it is important to establish the algebraic nature of physical quantities in a pre-metric space.
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© 1996 Birkhäuser Boston
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Jancewicz, B. (1996). The Extended Grassmann Algebra of R3 . In: Baylis, W.E. (eds) Clifford (Geometric) Algebras. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4104-1_28
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DOI: https://doi.org/10.1007/978-1-4612-4104-1_28
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