Combinatorics and Graph Theory

    

Invitation to Hadamard Matrices

Authors: Teo Banica

An Hadamard matrix is a square matrix $Hin M_N(pm1)$ whose rows and pairwise orthogonal. More generally, we can talk about the complex Hadamard matrices, which are the square matrices $Hin M_N(mathbb C)$ whose entries are on the unit circle, $|H_{ij}|=1$, and whose rows and pairwise orthogonal. The main examples are the Fourier matrices, $F_N=(w^{ij})$ with $w=e^{2pi i/N}$, and at the level of the general theory, the complex Hadamard matrices can be thought of as being some sort of exotic, generalized Fourier matrices. We discuss here the basic theory of the Hadamard matrices, real and complex, with emphasis on the complex matrices, and their geometric and analytic aspects.

Comments: 400 Pages.

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Submission history

[v1] 2019-10-15 11:22:08
[v2] 2021-07-27 09:29:30
[v3] 2024-07-29 17:05:47

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