A connection between Hadamard matrices, oriented hypergraphs and signed graphs
| Autor: | Howard Skogman, Nathan Reff |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Numerical Analysis Algebra and Number Theory Hadamard three-lines theorem Hadamard's maximal determinant problem 0211 other engineering and technologies 021107 urban & regional planning 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Hadamard's inequality Combinatorics Paley construction Integer matrix Complex Hadamard matrix Discrete Mathematics and Combinatorics Hadamard product Geometry and Topology 0101 mathematics Hadamard matrix Mathematics |
| Zdroj: | Linear Algebra and its Applications. 529:115-125 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2017.04.012 |
| Popis: | Matrices associated to oriented hypergraphs produce a connection between signed graphs and Hadamard matrices. The existence of a family of signed graphs that are switching equivalent to − K n and whose adjacency matrices sum to the zero matrix is shown to be equivalent to the existence of a Hadamard matrix. This equivalent problem is used to make explicit signed graph constructions which specialize to known Hadamard constructions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect