Clifford matrices and a problem of hurwitz
Clifford matrices and a problem of hurwitz
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Clifford 矩阵和 hurwitz 问题
DOI：
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发表时间：
2000
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通讯作者：
N. Anghel
中科院分区：
文献类型：
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作者：
N. Anghel
对于固定整数r，s > 0，找到存在赋范双线性形式的最小正整数n是一个一百年前的公开问题，起源于Hurwitz。它的答案在几种情况下是已知的，特别是对于小的r值（r≤9）。在本文中，我们确定它的大值的s关于r。所需的赋范双线性形式的显式建设涉及一个非常特殊的矩阵表示的真实的Clifford代数Cm和极小的范围是一个后果的Hopf-Stiefel准则。
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.