Geometric Analogy and Products of Vectors in <i>n</i>Dimensions

• 作者: Leonardo Simal Moreira
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Cross PRODUCT Space IRn Determinants GEOMETRIC ANALOGY Eckman’s PRODUCT
• 年，卷（期）: 2013,（1）
• 页码范围: 1-6
• 页数: 6页
• 分类号: O1

摘要

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, based?on known properties of determinants.