A sign pattern that allows oppositely signed orthogonal matrices

2012/12/25 by Bryan L. Shader, Shader, Bryan L., Chanyoung Lee Shader +2
Computer Science · Engineering · Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #graph theory and CDMA systems #math.CO #msc:05C50

paper · pdf · doi:10.48550/arxiv.1212.6062

arxiv created 2012/12/25 · openalex publication_date 2012/12/25 · arxiv updated 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 det Q₁=1 and det 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).

Related

• Sign Patterns of Orthogonal Matrices and the Strong Inner Product Property
• Orthogonal realizations of random sign patterns and other applications of the SIPP
• A generalization of Alternating Sign Matrices
• Sign-restricted matrices of 0's, 1's, and -1's
• Patterns of Alternating Sign Matrices