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https://doi.org/10.1016/0024-3795(92)90280-n
Copy DOIJournal: Linear Algebra and its Applications | Publication Date: Mar 1, 1992 |
License type: publisher-specific-oa |
Let G( n) denote the class of all symmetric matrices of order n with zero diagonal and off-diagonal entries ±1. For any C ϵ G( n), let f( C) denote a maximum eigenvalue of C 2, and define g( n) = min{ f;( C): C ϵ G( n)}. Let n≡2 (mod 4). The following two results are proved: (i) Suppose there exists an orthogonal matrix in G( n+4) but not in G( n). Then g( n) = g( n−1 = g( n−2) = n+3. (ii) Let C ϵ G( n) be a matrix for which the bound g( n)= n+3 is attained. Then, if C has a pair of rows whose inner product is ±2, C can be embedded as a principal submatrix of an orthogonal matrix in G( n+4). The case when an orthogonal matrix exists in G( n) has already been investigated by Cameron, Delsarte, and Goethals.
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