Geodesic
Rational orthogonal versus real orthogonal
The electronic journal of linear algebra, Tome 18 (2009), pp. 649-673.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The main question raised here is the following one: Given a real orthogonal n $\times n$ 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 $\leq 5$. The related problem for symmetric orthogonal matrices is also considered.
Classification : 15A21, 15B10
Keywords: real and rational orthogonal matrices, zero-patterns, combinatorial orthogonality 
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     author = {Djokovi\'c, Dragomir \v{Z}. and Severini, Simone and Sz\"oll\H{o}si, Ferenc},
     title = {Rational orthogonal versus real orthogonal},
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Djoković, Dragomir Ž.; Severini, Simone; Szöllősi, Ferenc. Rational orthogonal versus real orthogonal. The electronic journal of linear algebra, Tome 18 (2009), pp. 649-673. http://geodesic.mathdoc.fr/item/ELA_2009__18__a10/