OAI/Probability/InvariantIsing/Cavity/CavityRetainedFrame.lean

GitHub source file

11 declarations, 0 contain sorry, 0 declared as axioms

Complete the cavity directions inside each spectral group. The added columns are retained eigenvectors supported in the same group.

  1. def OAI.InvariantIsing.cavityGroupLift line 13
  2. lemma OAI.InvariantIsing.cavityGroupLift_support line 18
  3. lemma OAI.InvariantIsing.cavityGroupLift_gram line 23
  4. lemma OAI.InvariantIsing.cavityGroupLift_restrict line 42
  5. lemma OAI.InvariantIsing.cavityNormalizeFrame_spectral_support line 51
  6. lemma OAI.InvariantIsing.cavity_complement_projection line 60
  7. lemma OAI.InvariantIsing.cavityGroupLift_projection line 75
  8. theorem OAI.InvariantIsing.cavityRetainedFrame_exists line 105
  9. lemma OAI.InvariantIsing.cavitySpectralSupport_crossGram line 133
  10. lemma OAI.InvariantIsing.cavitySpectralSupport_eigen line 147
  11. lemma OAI.InvariantIsing.cavitySpectralProjectors_sum line 158