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Discussiones Mathematicae General Algebra and Applications 21(1) (2001) 67-82
DOI: https://doi.org/10.7151/dmgaa.1028

THE VECTOR CROSS PRODUCT FROM AN ALGEBRAIC POINT OF VIEW

Götz Trenkler

Department of Statistics, University of Dortmund
Vogelpothsweg 87, D-44221 Dortmund, Germany
e-mail:trenkler@amadeus.statistik.uni-dortmund.de

Abstract

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.

2000 Mathematics Subject Classification: Primary 15A72, Secondary 15A9.

References

[1]	A. Ben-Israel, and T.N.E. Greville, Generalized Inverses: Theory and Applications, John Wiley & Sons, New York 1974.
[2]	L.G. Chambers, A Course in Vector Analysis, Chapman and Hall, London 1969.
[3]	B. Hague, An Introduction to Vector Analysis for Physicists and Engineers, (6th edition, revised by D. Martin), Methuen & Science Paperbacks, London 1970.
[4]	T. Lancaster, and M. Tismenetsky, The Theory of Matrices. Academic Press, New York 1985.
[5]	E.A. Milne, Vectorial Mechanics, Methuen & Co. Ltd., London 1965.
[6]	C.R. Rao, and S.K. Mitra, Generalized Inverse of Matrices and its Applications, John Wiley & Sons, New York 1971.
[7]	T.G. Room, The composition of rotations in Euclidean three-space, Amer. Math. Monthly 59 (1952), 688-692.

Received 26 October 1999
Revised 11 February 2000