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Merge branch 'JointEigenspacesTuples' of https://github.com/leanprove…
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…r-community/mathlib4 into JointEigenspacesTuples
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j-loreaux committed Sep 24, 2024
2 parents 35ccbf3 + d0f0283 commit c223fef
Showing 1 changed file with 2 additions and 2 deletions.
4 changes: 2 additions & 2 deletions Mathlib/Analysis/InnerProductSpace/JointEigenspace.lean
Original file line number Diff line number Diff line change
Expand Up @@ -83,11 +83,11 @@ theorem iSup_eigenspace_inf_eigenspace (hB : B.IsSymmetric) (hAB : Commute A B)
(⨆ γ, eigenspace A α ⊓ eigenspace B γ) = eigenspace A α := by
conv_rhs => rw [← (eigenspace A α).map_subtype_top]
simp only [← Module.End.genEigenspace_one B, ← Submodule.map_iSup,
(eigenspace A α).inf_genEigenspace _ (eigenspace_invariant_of_commute hAB _)]
(eigenspace A α).inf_genEigenspace _ (mapsTo_genEigenspace_of_comm hAB α 1)]
congr 1
simpa only [Module.End.genEigenspace_one, Submodule.orthogonal_eq_bot_iff]
using orthogonalComplement_iSup_eigenspaces_eq_bot <|
hB.restrict_invariant <| eigenspace_invariant_of_commute hAB α
hB.restrict_invariant <| mapsTo_genEigenspace_of_comm hAB α 1

/-- If A and B are commuting symmetric operators acting on a finite dimensional inner product space,
then the simultaneous eigenspaces of A and B exhaust the space. -/
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