A characterization of skew Hadamard matrices and doubly regular tournaments

TL;DR

This paper introduces a novel way to characterize skew Hadamard matrices by analyzing the spectral data of tournaments of size n-2, providing new insights into their structure.

Contribution

It offers a new spectral characterization of skew Hadamard matrices based on tournament spectra, advancing understanding of their properties.

Findings

Spectral data of tournaments can determine skew Hadamard matrices.

New characterization links matrix properties to tournament spectra.

Provides a basis for further classification of Hadamard matrices.

Abstract

We give a new characterization of skew Hadamard matrices of size $n$ in terms of the data of the spectra of tournaments of size $n-2$.