Geodesic
$\pm$ sign pattern matrices that allow orthogonality
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 969-979 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A sign pattern $A$ is a $\pm $ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $\pm $ sign patterns with $n-1 \le N_-(A) \le n+1$ to allow orthogonality.
A sign pattern $A$ is a $\pm $ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $\pm $ sign patterns with $n-1 \le N_-(A) \le n+1$ to allow orthogonality.
Classification : 15A18, 15A36, 15A48, 15A99
Keywords: sign pattern; orthogonality; orthogonal matrix 
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Shao, Yanling; Sun, Liang; Gao, Yubin. $\pm$ sign pattern matrices that allow orthogonality. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 969-979. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a15/

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