Towards a classification of $6\times 6$ complex Hadamard matrices
| dc.creator | Matolcsi, Máté | |
| dc.creator | Szöllősi, Ferenc | |
| dc.date | 2007-02-02 | |
| dc.date.accessioned | 2026-07-07T07:44:30Z | |
| dc.date.available | 2026-07-07T07:44:30Z | |
| dc.description | Complex Hadamard matrices have received considerable attention in the past few years due to their appearance in quantum information theory. While a complete characterization is currently available only up to order 5 (in \cite{haagerup}), several new constructions of higher order matrices have appeared recently \cite{dita, karol, BN, MM, sz}. In particular, the classification of {\it self-adjoint} complex Hadamard matrices of order 6 was completed by Beuachamp and Nicoara in \cite{BN}, providing a previously unknown non-affine one-parameter orbit. In this paper we classify all \emph{dephased, symmetric} complex Hadamard matrices \emph{with real diagonal} of order 6. Furthermore, relaxing the condition on the diagonal entries we obtain a new non-affine one-parameter orbit connecting the Fourier matrix $F_6$ and Diţă's matrix $D_6$. This answers a recent question of Bengtsson & al. in \cite{BB}. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702043 | |
| dc.identifier | http://arxiv.org/abs/math/0702043 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123219 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Operator Algebras | |
| dc.subject | 05B20, 46L10 | |
| dc.title | Towards a classification of $6\times 6$ complex Hadamard matrices | |
| dc.type | text |