Abstract
Finding the least positive integer n for which there exists, for fixed integers r,s > 0, a normed bilinear form is a hundred year old open problem originating with Hurwitz. Its answer is known in several cases, in particular for small values of r(r≤9). In this paper we determine it for large values of s with respect to r. The explicit construction of the required normed bilinear forms involves a very special matrix representation of the real Clifford algebra Cm and the minimality of their ranges is a consequence of the Hopf-Stiefel criterion.
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