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Orthogonal Matrices with Zero Diagonal

Published online by Cambridge University Press:  20 November 2018

J. M. Goethals  and
J. J. Seidel
J. M. Goethals
Affiliation:
M.B.L.E. Research Laboratory, Brussels, Belgium, and Technological University, Eindhoven, Netherlands
J. J. Seidel
Affiliation:
M.B.L.E. Research Laboratory, Brussels, Belgium, and Technological University, Eindhoven, Netherlands
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The central problem in the present paper is the construction of symmetric and of skew-symmetric ( = skew) matrices C of order v, with diagonal elements 0 and other elements + 1 or — 1, satisfying

The following necessary conditions are known: v ≡ 2 (mod 4) and

a and b integers, for symmetric matrices C (Belevitch (1, 2), Raghavarao (14)), and v = 2 or v ≡ 0 (mod 4) for skew matrices C.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1001 - 1010
Copyright
Copyright © Canadian Mathematical Society 1967

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