A sign pattern that allows oppositely signed orthogonal matrices

Bryan L. Shader; Chanyoung L. Shader

arxiv: 1212.6062 · v1 · pith:NC7S2T7Snew · submitted 2012-12-25 · 🧮 math.CO

A sign pattern that allows oppositely signed orthogonal matrices

Bryan L. Shader , Chanyoung L. Shader This is my paper

classification 🧮 math.CO

keywords matricespatternsignorthogonalalgebraallowallowsapplications

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We provide the first example of a sign pattern $S$ for which there exist orthogonal matrices $Q_1$ and $Q_2$ with sign pattern $S$ such that $\det Q_1=1$ and $\det Q_2=-1$. 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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A sign pattern that allows oppositely signed orthogonal matrices

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