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

  • Paul Y. H. Yiu (a1)

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.

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Mathematical Proceedings of the Cambridge Philosophical Society
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  • EISSN: 1469-8064
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