On Some Quaternionic Hadamard Matrices of Small Order
Combinatorics
2022-03-08 v2 Rings and Algebras
Abstract
We introduce Hadamard matrices whose entries are quaternionic. We then go on to provide classification of quaternionic Hadamard matrices of circulant core of orders 2 through 5. We also introduce quaternionic Hadamard matrices of Butson type and ways to create quaternionic Hadamard matrices from real and complex Hadamard matrices. Examples are shown that showcase how Hadamard matrices over the quaternions are richer than Hadamard matrices over the complex numbers.
Keywords
Cite
@article{arxiv.2112.09613,
title = {On Some Quaternionic Hadamard Matrices of Small Order},
author = {Logan M. Higginbotham and Chase T. Worley},
journal= {arXiv preprint arXiv:2112.09613},
year = {2022}
}
Comments
30 pages, submitted for publication