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Regular complex Hadamard matrices of order 7,8

Contributed by Teo Banica

A complex Hadamard matrix $H\in M_N(\mathbb C)$ is called regular when the scalar products between its rows $\sum_kH_{ik}\bar{H}_{jk}=0$ decompose as trivially vanishing sums of roots of unity, rotated by scalars. We review the general theory of such matrices, including the known classification at $N=6$ , and then we work out classification results at $N=7$ and $N=8$ .

Primarily AI-generated textHuman understanding: some partsButson matrixHadamard matrix

Nov 06, 202664 pages

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Regular complex Hadamard matrices of order 7,8

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