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Vector products*

Published online by Cambridge University Press:  01 August 2016

F. Gerrish
F. Gerrish*
Affiliation:
43 Roman's Way, Pyrford, Woking GU22 8TR
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Extract

In his thought-provoking Note 82.45 (November 1998) about products of vectors, Bob Ardler asks (p. 454) “Why does dot thrive in n dimensions, but cross only in 3?” and (p. 456) “Which, if any, generalisations of the cross product have been pursued?”

Both of these matters have been treated fairly recently in several journals, including the Gazette, but the subject was first discussed and completely settled in 1942 by B. Eckmann in [1] (see especially pp. 338-339); cf. also [2].

Type
Articles
Information
The Mathematical Gazette , Volume 84 , Issue 501 , November 2000 , pp. 453 - 459
Copyright
Copyright © The Mathematical Association 2000

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Footnotes

*

A small part of the material in this article was offered as a ‘short presentation’ during the 1994 MA Conference at Royal Holloway College.

References

1. Eckmann, B. Stetige Lösungen linearer Gleichungssysteme, Comment. Math. Helv. 15 (1942–43) pp. 318–339.Google Scholar
2. Brown, R. B. and Gray, A. Vector cross products, Comment. Math. Helv. 42 (1967) pp. 222–236.CrossRefGoogle Scholar
3. Massey, W. S. Cross products of vectors in higher-dimensional euclidean spaces, Amer. Math. Mon. 90 (1983) pp. 697–700.CrossRefGoogle Scholar
4. Gerrish, F. Ordered pairs, Math. Gaz. 79 (March 1995) pp. 30–46.Google Scholar
5. Ewing, J. H. (ed.), Numbers, Springer (1991).Google Scholar
6. Walsh, B. The scarcity of cross products on euclidean spaces, Amer. Math. Mon. 74 (1967) pp. 188–194.Google Scholar
7. Jacobson, N. Basic algebra I, 2nd edition, Freeman (1985).Google Scholar
8. Shaw, R. and Yeadon, F. J. On (a × b) × c, Amer. Math. Mon. 96 (1989) pp. 623–629.Google Scholar
9. Whittle, A. A vector n-tuple product, Math. Gaz. 65 (March 1981) pp. 47–49.Google Scholar
10. Dittmer, A. Cross product identities in arbitrary dimension, Amer. Math. Mon. 101 (1994) pp. 887–891.Google Scholar
11. Shaw, R. Vector cross products in n dimensions, Int. J. Math. Educ. Sci. Technol. 18 (1987) pp. 803–816.CrossRefGoogle Scholar
12. Zvengrowski, P. A 3-fold vector product on Comment. Math. Helv. 40 (1965–66) pp. 149–152.Google Scholar
13. Shaw, R. Ternary vector cross products, J. Phys. A:Math. Gen. 20 (1987) pp. L689-L694.CrossRefGoogle Scholar
14. Russell, B. Introduction to mathematical philosophy, 2nd edition, Allen & Unwin and Macmillan (1920).Google Scholar