Just to clarify Michel's earlier remark, the field norm for the cyclotomics defines the norm in which these vectors are equiangular, and then they will generally **not** be equiangular in the standard norm based on the Hilbert-Schmidt inner product. In the example that he quotes,
$$\|(7\pm 3 \sqrt{5})/32\|_{\mathbb{Q}(\sqrt{5})} = \left[\frac{(7\pm 3 \sqrt{5})}{32} \frac{(7\mp 3 \sqrt{5})}{32}\right]^{1/\deg(\mathbb{Q}[\sqrt{5})]} = \frac{1}{16}.$$
It might be helpful in v2 of the paper if these vectors are called "generalized equiangular" or "equiangular with respect to the field norm", as this will help avoid confusion.
Just to clarify Michel's earlier remark, the field norm for the cyclotomics defines the norm in which these vectors are equiangular, and then they will generally **not** be equiangular in the standard norm based on the Hilbert-Schmidt inner product. In the example that he quotes,
$$\|(7\pm 3 \sqrt{5})/32\|_{\mathbb{Q}(\sqrt{5})} = \left[\frac{(7\pm 3 \sqrt{5})}{32} \frac{(7\mp 3 \sqrt{5})}{32}\right]^{1/\deg(\mathbb{Q}[\sqrt{5})]} = \frac{1}{16}.$$
It might be helpful in v2 of the paper if these vectors are called "generalized equiangular" or "equiangular with respect to the the field norm", as this will help avoid confusion.
Braneshop, and
the US National Science Foundation.
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