A sign pattern that allows oppositely signed orthogonal matrices

Bryan L. Shader; Chanyoung L. Shader

paper

A sign pattern that allows oppositely signed orthogonal matrices

arXiv:1212.6062

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).