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K-Vectors and Wedge Products

In: An Introduction to Multivariable Analysis from Vector to Manifold

Author

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  • Piotr Mikusiński

    (University of Central Florida, Department of Mathematics)

  • Michael D. Taylor

    (University of Central Florida, Department of Mathematics)

Abstract

When it is first encountered, the wedge product may appear both artificial and exotic. This appearance is deceptive. The wedge product is something like a generalization of the cross product of 3-dimensional vectors, so it should not be surprising that things looking like wedge products should arise in natural phenomena. Certain wedge products, the simple K-vectors, have striking geometric interpretations with a strong connection to determinants and oriented volume, so that the wedge product is an excellent tool for analytic geometry in Euclidean Spaces of arbitrary dimension. This connection with geometry leads in turn to an elegant and marvelously unified language for calculus not simply in Euclidean Spaces but in manifolds. It is this last aspect of the theory of wedge products which draws us to its study.

Suggested Citation

  • Piotr Mikusiński & Michael D. Taylor, 2002. "K-Vectors and Wedge Products," Springer Books, in: An Introduction to Multivariable Analysis from Vector to Manifold, chapter 6, pages 189-217, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0073-4_6
    DOI: 10.1007/978-1-4612-0073-4_6
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