Abstract.
A ± sign pattern is a matrix whose entries are in the set {+,−}. An n×n ± sign pattern A allows orthogonality if there exists a real orthogonal matrix B in the qualitative class of A. In this paper, we prove that for n≥3 there is an n×n ± sign pattern A allowing orthogonality with exactly k negative entries if and only if n−1≤k≤n2−n+1.
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Research supported by Shanxi Natural Science Foundation 20011006, 20041010
Final version received: October 22, 2003
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Gao, Y., Shao, Y. The Number of Negative Entries in a Sign Pattern Allowing Orthogonality. Graphs and Combinatorics 20, 311–317 (2004). https://doi.org/10.1007/s00373-004-0575-y
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DOI: https://doi.org/10.1007/s00373-004-0575-y