Construction, classification and parametrization of complex Hadamard matrices

TL;DR

This paper provides a comprehensive overview of complex Hadamard matrices, covering their theory, recent advances, and applications across various mathematical tools and fields.

Contribution

It offers a detailed synthesis of the current state-of-the-art in complex Hadamard matrices, including classification, construction, and parametrization methods.

Findings

Recent classification results of complex Hadamard matrices

New parametrization techniques for these matrices

Applications in combinatorics, functional analysis, and symbolic computation

Abstract

The intended purpose of this work is to provide the reader with a comprehensive, state-of-the art presentation of the theory of complex Hadamard matrices, or at least report on the very recent advances. This manuscript consists of three chapters, each describing one of three distinct faces of this field whose treatment require various mathematical tools ranging from combinatorics, functional analysis to symbolic computation. Although we firmly believe that these beautiful objects are interesting on their own and worth investigating from a purely mathematical perspective we make considerable efforts to highlight some of their applications we aware of.