A sign pattern that allows oppositely signed orthogonal matrices

Bryan L. Shader; Chanyoung L. Shader

A sign pattern that allows oppositely signed orthogonal matrices

Combinatorics 2012-12-27 v1

Authors: Bryan L. Shader , Chanyoung L. Shader

Abstract

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).

Keywords

hadamard matrices

Cite

@article{arxiv.1212.6062,
  title  = {A sign pattern that allows oppositely signed orthogonal matrices},
  author = {Bryan L. Shader and Chanyoung L. Shader},
  journal= {arXiv preprint arXiv:1212.6062},
  year   = {2012}
}

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