Manuscript Em06-B@1 · Em06-B-v1.tex · section · 61e38859

Finite families: spectral laws versus ordered Weyl correlations

Finite families: spectral laws versus ordered Weyl correlations · lines 836–851

Em06-B@1#eq:SA

Fix real $f_{1}, \dots, f_{J}$ , with common $h, χ, z$ , and write

v_{j} = v (f_{j}, h, χ), o_{j} = 2 Re ⟨ v_{j}, z ⟩, O_{j, ϵ} = ϵ Φ (v_{j}) .

Define the real matrices

S_{ij} = Re ⟨ v_{i}, v_{j} ⟩, A_{ij} = Im ⟨ v_{i}, v_{j} ⟩ .

The matrix $S$ is positive semidefinite and $A$ is antisymmetric.

Displayed formulas in this passage

Em06-B@1#eq:SA · line 845
$S_{ij} = Re ⟨ v_{i}, v_{j} ⟩, A_{ij} = Im ⟨ v_{i}, v_{j} ⟩ .$
unlabeled · line 839
$v_{j} = v (f_{j}, h, χ), o_{j} = 2 Re ⟨ v_{j}, z ⟩, O_{j, ϵ} = ϵ Φ (v_{j}) .$