A sign pattern that allows oppositely signed orthogonal matrices
Abstract
We provide the first example of a sign pattern S for which there exist orthogonal matrices Q1 and Q2 with sign pattern S such that Q1=1 and Q2=-1. The existence of such matrices is raised by C. Waters in "Sign Pattern Matrices That Allow Orthogonality", Linear Algebra and Its Applications, 235:1-13 (1996).
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