P. Gritzmann and V. Klee, “On the Complexity of Some Basic Problems in Computational Convexity II. Volume and Mixed Volumes,” In: T. Bisztriczky, P. McMuffen, R. Schneider and A. W. Weiss, Eds., Polytopes: Abstract, Convex and Computational, Kluwer, Dordrecht, 1994, p. 29.

has been cited by the following article:

• TITLE: Geometric Analogy and Products of Vectors in n Dimensions

  AUTHORS: Leonardo Simal Moreira

  KEYWORDS: Cross Product; Space IRn; Determinants; Geometric Analogy; Eckman’s Product

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.3 No.1, March 27, 2013

  ABSTRACT: The cross product in Euclidean space IR3 is an operation in which two vectors are associated to generate a third vector, also in space IR3. This product can be studied rewriting its basic equations in a matrix structure, more specifically in terms of determinants. Such a structure allows extending, for analogy, the ideas of the cross product for a type of the product of vectors in higher dimensions, through the systematic increase of the number of rows and columns in determinants that constitute the equations. So, in a n-dimensional space with Euclidean norm, we can associate n – 1 vectors and to obtain an n-th vector, with the same geometric characteristics of the product in three dimensions. This kind of operation is also a geometric interpretation of the product defined by Eckman [1]. The same analogies are also useful in the verification of algebraic properties of such products, basedon known properties of determinants.