Geodesic
The vector cross product from an algebraic point of view
Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 67-82

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The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
Keywords: vector cross product, generalized inverse, Moore-Penrose inverse, linear equations 
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Trenkler, Götz. The vector cross product from an algebraic point of view. Discussiones Mathematicae. General Algebra and Applications, Tome 21 (2001) no. 1, pp. 67-82. http://geodesic.mathdoc.fr/item/DMGAA_2001_21_1_a6/