Invitation to Hadamard matrices

Teo Banica (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

A complex Hadamard matrix is a square matrix $H\in M_N(\mathbb C)$ whose entries are on the unit circle, $|H_{ij}|=1$, and whose rows and pairwise orthogonal. The main example is the Fourier matrix, $F_N=(w^{ij})$ with $w=e^{2\pi i/N}$. We discuss here the basic theory of such matrices, with emphasis on geometric and analytic aspects.

Domaines: Algèbres d'opérateurs [math.OA]

Teo Banica. Invitation to Hadamard matrices. 2022. ⟨hal-02317067v4⟩