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bump to nightly-2023-04-04-16
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leanprover-community-bot committed Apr 4, 2023
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5 changes: 2 additions & 3 deletions Mathbin/Analysis/Calculus/LagrangeMultipliers.lean
Original file line number Diff line number Diff line change
Expand Up @@ -78,9 +78,8 @@ theorem IsLocalExtrOn.exists_linear_map_of_hasStrictFderivAt
-- squeezed `simp [mul_comm]` to speed up elaboration
simp only [mul_comm, Algebra.id.smul_eq_mul, LinearEquiv.trans_apply, LinearEquiv.prod_apply,
LinearEquiv.refl_apply, LinearMap.ringLmapEquivSelf_symm_apply, LinearMap.coprodEquiv_apply,
ContinuousLinearMap.toLinearMap_eq_coe, ContinuousLinearMap.coe_prod,
LinearMap.coprod_comp_prod, LinearMap.add_apply, LinearMap.coe_comp,
ContinuousLinearMap.coe_coe, LinearMap.coe_smulRight, LinearMap.one_apply]
[anonymous], ContinuousLinearMap.coe_prod, LinearMap.coprod_comp_prod, LinearMap.add_apply,
LinearMap.coe_comp, ContinuousLinearMap.coe_coe, LinearMap.coe_smulRight, LinearMap.one_apply]
#align is_local_extr_on.exists_linear_map_of_has_strict_fderiv_at IsLocalExtrOn.exists_linear_map_of_hasStrictFderivAt

/-- Lagrange multipliers theorem: if `φ : E → ℝ` has a local extremum on the set `{x | f x = f x₀}`
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9 changes: 4 additions & 5 deletions Mathbin/Analysis/InnerProductSpace/PiL2.lean
Original file line number Diff line number Diff line change
Expand Up @@ -887,9 +887,9 @@ noncomputable def LinearIsometry.extend (L : S →ₗᵢ[𝕜] V) : V →ₗᵢ[
rw [← sq_eq_sq (norm_nonneg _) (norm_nonneg _), norm_sq_eq_add_norm_sq_projection x S]
simp only [sq, Mx_decomp]
rw [norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zero (L (p1 x)) (L3 (p2 x)) Mx_orth]
simp only [LinearIsometry.norm_map, p1, p2, ContinuousLinearMap.toLinearMap_eq_coe,
add_left_inj, mul_eq_mul_left_iff, norm_eq_zero, true_or_iff, eq_self_iff_true,
ContinuousLinearMap.coe_coe, Submodule.coe_norm, Submodule.coe_eq_zero]
simp only [LinearIsometry.norm_map, p1, p2, [anonymous], add_left_inj, mul_eq_mul_left_iff,
norm_eq_zero, true_or_iff, eq_self_iff_true, ContinuousLinearMap.coe_coe, Submodule.coe_norm,
Submodule.coe_eq_zero]
exact
{ toLinearMap := M
norm_map' := M_norm_map }
Expand All @@ -898,8 +898,7 @@ noncomputable def LinearIsometry.extend (L : S →ₗᵢ[𝕜] V) : V →ₗᵢ[
theorem LinearIsometry.extend_apply (L : S →ₗᵢ[𝕜] V) (s : S) : L.extend s = L s :=
by
haveI : CompleteSpace S := FiniteDimensional.complete 𝕜 S
simp only [LinearIsometry.extend, ContinuousLinearMap.toLinearMap_eq_coe, ←
LinearIsometry.coe_toLinearMap]
simp only [LinearIsometry.extend, [anonymous], ← LinearIsometry.coe_toLinearMap]
simp only [add_right_eq_self, LinearIsometry.coe_toLinearMap,
LinearIsometryEquiv.coe_toLinearIsometry, LinearIsometry.coe_comp, Function.comp_apply,
orthogonalProjection_mem_subspace_eq_self, LinearMap.coe_comp, ContinuousLinearMap.coe_coe,
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8 changes: 4 additions & 4 deletions Mathbin/Analysis/InnerProductSpace/Projection.lean
Original file line number Diff line number Diff line change
Expand Up @@ -705,8 +705,8 @@ def reflection : E ≃ₗᵢ[𝕜] E :=
convert norm_sub_eq_norm_add this using 2
· rw [LinearEquiv.coe_mk, reflectionLinearEquiv, LinearEquiv.toFun_eq_coe,
LinearEquiv.coe_ofInvolutive, LinearMap.sub_apply, LinearMap.id_apply, bit0,
LinearMap.add_apply, LinearMap.comp_apply, Submodule.subtype_apply,
ContinuousLinearMap.toLinearMap_eq_coe, ContinuousLinearMap.coe_coe]
LinearMap.add_apply, LinearMap.comp_apply, Submodule.subtype_apply, [anonymous],
ContinuousLinearMap.coe_coe]
dsimp [w, v]
abel
· simp only [add_sub_cancel'_right, eq_self_iff_true] }
Expand Down Expand Up @@ -1220,8 +1220,8 @@ theorem LinearIsometryEquiv.reflections_generate_dim_aux [FiniteDimensional ℝ
symm
ext x
have := LinearMap.congr_fun (linear_map.ker_eq_top.mp this) x
simpa only [sub_eq_zero, ContinuousLinearMap.toLinearMap_eq_coe, ContinuousLinearMap.coe_sub,
LinearMap.sub_apply, LinearMap.zero_apply] using this
simpa only [sub_eq_zero, [anonymous], ContinuousLinearMap.coe_sub, LinearMap.sub_apply,
LinearMap.zero_apply] using this
· -- Inductive step. Let `W` be the fixed subspace of `φ`. We suppose its complement to have
-- dimension at most n + 1.
let W := ker (ContinuousLinearMap.id ℝ F - φ)
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2 changes: 1 addition & 1 deletion Mathbin/Analysis/NormedSpace/Dual.lean
Original file line number Diff line number Diff line change
Expand Up @@ -102,7 +102,7 @@ theorem double_dual_bound (x : E) : ‖(inclusionInDoubleDual 𝕜 E) x‖ ≤

/-- The dual pairing as a bilinear form. -/
def dualPairing : Dual 𝕜 E →ₗ[𝕜] E →ₗ[𝕜] 𝕜 :=
ContinuousLinearMap.coeLm 𝕜
ContinuousLinearMap.coeLM 𝕜
#align normed_space.dual_pairing NormedSpace.dualPairing

@[simp]
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2 changes: 1 addition & 1 deletion Mathbin/Analysis/NormedSpace/FiniteDimension.lean
Original file line number Diff line number Diff line change
Expand Up @@ -178,7 +178,7 @@ theorem ContinuousLinearMap.continuous_det : Continuous fun f : E →L[𝕜] E =
refine' Continuous.matrix_det _
exact
((LinearMap.toMatrix b b).toLinearMap.comp
(ContinuousLinearMap.coeLm 𝕜)).continuous_of_finiteDimensional
(ContinuousLinearMap.coeLM 𝕜)).continuous_of_finiteDimensional
· unfold LinearMap.det
simpa only [h, MonoidHom.one_apply, dif_neg, not_false_iff] using continuous_const
#align continuous_linear_map.continuous_det ContinuousLinearMap.continuous_det
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31 changes: 15 additions & 16 deletions Mathbin/Analysis/NormedSpace/Multilinear.lean
Original file line number Diff line number Diff line change
Expand Up @@ -1027,17 +1027,17 @@ def ContinuousLinearEquiv.compContinuousMultilinearMapL (g : G ≃L[𝕜] G') :
left_inv := by
intro f
ext1 m
simp only [comp_continuous_multilinear_mapL, ContinuousLinearEquiv.coe_def_rev,
to_linear_map_eq_coe, LinearMap.toFun_eq_coe, coe_coe, LinearMap.mkContinuous₂_apply,
LinearMap.mk₂_apply, comp_continuous_multilinear_map_coe, ContinuousLinearEquiv.coe_coe,
Function.comp_apply, ContinuousLinearEquiv.symm_apply_apply]
simp only [comp_continuous_multilinear_mapL, [anonymous], to_linear_map_eq_coe,
LinearMap.toFun_eq_coe, coe_coe, LinearMap.mkContinuous₂_apply, LinearMap.mk₂_apply,
comp_continuous_multilinear_map_coe, ContinuousLinearEquiv.coe_coe, Function.comp_apply,
ContinuousLinearEquiv.symm_apply_apply]
right_inv := by
intro f
ext1 m
simp only [comp_continuous_multilinear_mapL, ContinuousLinearEquiv.coe_def_rev,
to_linear_map_eq_coe, LinearMap.mkContinuous₂_apply, LinearMap.mk₂_apply,
LinearMap.toFun_eq_coe, coe_coe, comp_continuous_multilinear_map_coe,
ContinuousLinearEquiv.coe_coe, Function.comp_apply, ContinuousLinearEquiv.apply_symm_apply]
simp only [comp_continuous_multilinear_mapL, [anonymous], to_linear_map_eq_coe,
LinearMap.mkContinuous₂_apply, LinearMap.mk₂_apply, LinearMap.toFun_eq_coe, coe_coe,
comp_continuous_multilinear_map_coe, ContinuousLinearEquiv.coe_coe, Function.comp_apply,
ContinuousLinearEquiv.apply_symm_apply]
continuous_toFun := (compContinuousMultilinearMapL 𝕜 _ _ _ g.toContinuousLinearMap).Continuous
continuous_invFun :=
(compContinuousMultilinearMapL 𝕜 _ _ _ g.symm.toContinuousLinearMap).Continuous }
Expand Down Expand Up @@ -1201,8 +1201,8 @@ theorem norm_comp_continuous_linearIsometry_le (g : ContinuousMultilinearMap
by
apply op_norm_le_bound _ (norm_nonneg _) fun m => _
apply (g.le_op_norm _).trans _
simp only [ContinuousLinearMap.toLinearMap_eq_coe, ContinuousLinearMap.coe_coe,
LinearIsometry.coe_toContinuousLinearMap, LinearIsometry.norm_map]
simp only [[anonymous], ContinuousLinearMap.coe_coe, LinearIsometry.coe_toContinuousLinearMap,
LinearIsometry.norm_map]
#align continuous_multilinear_map.norm_comp_continuous_linear_isometry_le ContinuousMultilinearMap.norm_comp_continuous_linearIsometry_le

theorem norm_comp_continuous_linearIsometryEquiv (g : ContinuousMultilinearMap 𝕜 E₁ G)
Expand Down Expand Up @@ -1269,15 +1269,14 @@ def compContinuousLinearMapEquivL (f : ∀ i, E i ≃L[𝕜] E₁ i) :
left_inv := by
intro g
ext1 m
simp only [ContinuousLinearMap.toLinearMap_eq_coe, LinearMap.toFun_eq_coe,
ContinuousLinearMap.coe_coe, comp_continuous_linear_mapL_apply,
comp_continuous_linear_map_apply, ContinuousLinearEquiv.coe_coe,
ContinuousLinearEquiv.apply_symm_apply]
simp only [[anonymous], LinearMap.toFun_eq_coe, ContinuousLinearMap.coe_coe,
comp_continuous_linear_mapL_apply, comp_continuous_linear_map_apply,
ContinuousLinearEquiv.coe_coe, ContinuousLinearEquiv.apply_symm_apply]
right_inv := by
intro g
ext1 m
simp only [ContinuousLinearMap.toLinearMap_eq_coe, comp_continuous_linear_mapL_apply,
LinearMap.toFun_eq_coe, ContinuousLinearMap.coe_coe, comp_continuous_linear_map_apply,
simp only [[anonymous], comp_continuous_linear_mapL_apply, LinearMap.toFun_eq_coe,
ContinuousLinearMap.coe_coe, comp_continuous_linear_map_apply,
ContinuousLinearEquiv.coe_coe, ContinuousLinearEquiv.symm_apply_apply] }
#align continuous_multilinear_map.comp_continuous_linear_map_equivL ContinuousMultilinearMap.compContinuousLinearMapEquivL

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7 changes: 7 additions & 0 deletions Mathbin/Analysis/NormedSpace/OperatorNorm.lean

Large diffs are not rendered by default.

88 changes: 88 additions & 0 deletions Mathbin/LinearAlgebra/Isomorphisms.lean

Large diffs are not rendered by default.

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