2004/04/18 by J. Richard Lundgren, Lundgren, Lundgren, J. Richard +5
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #05C20 #05C50 #Artificial Intelligence in Games #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Game Theory and Voting Systems #Quantum Physics (quant-ph) #Sports Analytics and Performance #math.CO #msc:05C20 #msc:05C50 #quant-ph
paper · pdf · doi:10.48550/arxiv.math/0404320
13 pages
arxiv created 2004/04/18 · openalex publication_date 2004/04/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be orthogonal is a property known as combinatorial orthogonality. If the adjacency matrix of a directed graph forms a pattern of a combinatorially orthogonal matrix, we say the digraph is quadrangular. We look at the quadrangular property in tournaments and regular tournaments.