Rational Orthogonal versus Real Orthogonal

Details Rational Orthogonal versus Real Orthogonal Rational Orthogonal versus Real Orthogonal

2009-03-16

arxiv.org/abs/0903.2853v1

Electronic Journal of Linear Algebra 18 (2009) 649-673

Mathematics

Combinatorics

23 pages

Scientific paper

The main question we raise here is the following one: given a real orthogonal
n by n matrix X, is it true that there exists a rational orthogonal matrix Y
having the same zero-pattern? We conjecture that this is the case and prove it
for n<=5. We also consider the related problem for symmetric orthogonal
matrices.

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