# Deformed Fourier matrices in bistochastic form

## TL;DR

This paper explores the properties of deformed Fourier matrices in bistochastic form, providing computations and insights into their structure and relation to complex Hadamard matrices.

## Contribution

It analyzes the deformation of Fourier matrices into bistochastic form, highlighting new structural insights and computational methods.

## Key findings

- Deformed Fourier matrices can be represented in bistochastic form.
- Explicit computations for basic deformations of Fourier matrices.
- Enhanced understanding of complex Hadamard matrices in bistochastic form.

## Abstract

Many interesting examples of complex Hadamard matrices $H\in M_N(\mathbb C)$ can be put, up to the standard equivalence relation for such matrices, in bistochastic form. We discuss here this phenomenon, with a number of computations for some of the most basic such matrices, namely the deformations of the Fourier matrix $F_N\in M_N(\mathbb C)$.

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Source: https://tomesphere.com/paper/1901.04941