2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106722Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for dimension N=2,...,16. In particular, we explicitly write down some families of complex Hadamard matrices for N=12,14 and 16, which we could not find in the existing literature.56 pages, no figures, an updated on line version at http://chaos.if.uj.edu.pl/~karol/hadamard/Quantum PhysicsCombinatoricsRings and Algebrastext