2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116359We construct new pairs of orthogonal maximal abelian $*$-subalgebras of $M_6(\mathbb C)$, by classifying all self-adjoint complex Hadamard matrices of order 6. In particular, we exhibit a non-affine one-parameter family of non-equivalent Hadamard matrices of order 6. In the last part of the paper we present other previously unknown examples of complex Hadamard matrices of higher orders.Operator AlgebrasCombinatoricsQuantum Physicstext