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chore(Algebra/Star/Unitary): rename unitary.spectrum.unitary_conjugate #30697

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chore(Algebra/Star/Unitary): rename unitary.spectrum.unitary_conjugate #30697

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e9c13a0
fix lemma names
themathqueen Oct 19, 2025
eeb5b96
fix
themathqueen Oct 19, 2025
3239f1d
Deprecate unitary_conjugate aliases
themathqueen Oct 20, 2025
d22e8f8
Update Unitary.lean
themathqueen Oct 20, 2025
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Apply suggestions from code review
themathqueen Oct 20, 2025
a81d974
Update Mathlib/Algebra/Star/Unitary.lean
themathqueen Oct 20, 2025
3870b0b
Update Mathlib/Algebra/Star/Unitary.lean
themathqueen Oct 20, 2025
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Apply suggestions from code review
themathqueen Oct 20, 2025
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15 changes: 10 additions & 5 deletions Mathlib/Algebra/Star/Unitary.lean
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Expand Up @@ -404,17 +404,22 @@ universe u

variable {R A : Type*} [CommSemiring R] [Ring A] [Algebra R A] [StarMul A]

/-- Unitary conjugation preserves the spectrum, star on left. -/
/-- Unitary conjugation preserves the spectrum, star on right. -/
@[simp]
lemma spectrum.unitary_conjugate {a : A} {u : unitary A} :
lemma _root_.spectrum.unitary_star_right_conjugate {a : A} {u : unitary A} :
spectrum R (u * a * (star u : A)) = spectrum R a :=
spectrum.units_conjugate (u := unitary.toUnits u)

/-- Unitary conjugation preserves the spectrum, star on right. -/
/-- Unitary conjugation preserves the spectrum, star on left. -/
@[simp]
lemma spectrum.unitary_conjugate' {a : A} {u : unitary A} :
lemma _root_.spectrum.unitary_star_left_conjugate {a : A} {u : unitary A} :
spectrum R ((star u : A) * a * u) = spectrum R a := by
simpa using spectrum.unitary_conjugate (u := star u)
simpa using spectrum.unitary_star_right_conjugate (u := star u)

@[deprecated (since := "2025-10-20")] alias spectrum.unitary_conjugate :=
spectrum.unitary_star_right_conjugate
@[deprecated (since := "2025-10-20")] alias spectrum.unitary_conjugate' :=
spectrum.unitary_star_left_conjugate

end UnitaryConjugate

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2 changes: 1 addition & 1 deletion Mathlib/LinearAlgebra/Matrix/HermitianFunctionalCalculus.lean
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Expand Up @@ -110,7 +110,7 @@ instance instContinuousFunctionalCalculus :
apply Set.eq_of_subset_of_subset
· rw [← ContinuousMap.spectrum_eq_range f]
apply AlgHom.spectrum_apply_subset
· rw [cfcAux_apply, unitary.spectrum.unitary_conjugate]
· rw [cfcAux_apply, spectrum.unitary_star_right_conjugate]
rintro - ⟨x, rfl⟩
apply spectrum.of_algebraMap_mem 𝕜
simp only [Function.comp_apply, Set.mem_range, spectrum_diagonal]
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