Rational orthogonal versus real orthogonal

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Dragomir Z. Djokovic
Simone Severini
Ferenc Szöllősi


The main question raised here is the following one: Given a real orthogonal n × n
matrix X, is it true that there exists a rational orthogonal matrix Y having the same zero-pattern? It is conjectured that this is the case and proved for n ≤ 5. The related problem for symmetric orthogonal matrices is also considered.

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