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Quadratic forms between spheres and the non-existence of sums of squares formulae

Published online by Cambridge University Press:  24 October 2008

Paul Y. H. Yiu
Paul Y. H. Yiu
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Y4, Canada
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Extract

Hurwitz [6] posed in 1898 the problem of determining, for given integers r and s, the least integer n, denoted by r s, for which there exists an [r, s, n] formula, namely a sums of squares formula of the type

where are bilinear forms with real coefficients in and . Such an [r, s, n] formula is equivalent to a normed bilinear map satisfying . We shall, therefore, speak of sums of squares formulae and normed bilinear maps interchangeably.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 493 - 504
Copyright
Copyright © Cambridge Philosophical Society 1986

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