a1 Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Y4, Canada
Hurwitz  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.
(Received January 09 1986)