%0 Journal Article
%T Geometric Analogy and Products of Vectors in <i>n</i> Dimensions
%A Leonardo Simal Moreira
%J Advances in Linear Algebra & Matrix Theory
%P 1-6
%@ 2165-3348
%D 2013
%I Scientific Research Publishing
%R 10.4236/alamt.2013.31001
%X <p>
	<span>The cross product in Euclidean space </span><i><span>IR</span></i><sup><span>3</span></sup><span> is an operation in which two vectors are associated to generate a third vector, also in space </span><i><span>IR</span></i><sup><span>3</span></sup><span>. 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 <i>n</i>-dimensional space with Euclidean norm, we can associate <i>n</i> ¨C 1 vectors and to obtain an <i>n</i>-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 [</span><span>1</span><span>]. The same analogies are also useful in the verification of algebraic properties of such products, based&nbsp;on known properties of determinants.</span><span></span> 
</p>
%K Cross Product
%K Space IRn
%K Determinants
%K Geometric Analogy
%K EckmanĄ¯s Product
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=29071