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Hurwitz on Hadamard designs

Published online by Cambridge University Press:  17 April 2009

T. Storer
T. Storer
Affiliation:
University of Michigan, Ann Arbor, Michigan, USA.
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Abstract

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An n × n–matrix on n signed variables is called Hadamard of Williamson type if each variable occurs exactly once in each row, and the inner product of any pair of distinct rows is zero. We show here that these matrices correspond in a natural way to rational formulas for products of sums of n squares, shown by Hurwitz to exist only for n = 1, 2, 4, and 8. Hurwitz' arguments contain an implicit proof that this correspondence is one-to-one (we show this directly) and hence that Hadamard matrices of Williamson type exist for orders 1, 2, 4 and 8 only.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 109 - 112
Copyright
Copyright © Australian Mathematical Society 1971

References

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