chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
9,389 | lean_file_chunk | 3e9769b6092fb1a34f5f890a57eb5625d8f58b5890859338a4d31ffd6890b134 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.Lemmas
import LeanPool.Monlib4.LinearAlgebra.LinearMapOp
import LeanPool.Monlib4.LinearAlgebra.Coalgebra.Lemmas
import ... |
435 | lean_file_chunk | 2bb15bff7220d4557c6689028da8f82b3a40137dd9cdd59c959d0bd561a2e160 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Coalgebra.FiniteDimensional
import LeanPool.Monlib4.LinearAlgebra.Coalgebra.Lemmas
import LeanPool.Monlib4.LinearAlgebra.Coalgebra.Mu... |
1,384 | lean_file_chunk | e427afbd81d284cdd583ac9b2acf79b217cd04cf33ea639ef5cbe82ca0cdf590 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Pi
import Mathlib.LinearAlgebra.Pi
-- import Mathlib.LinearAlgebra.ProjectiveSpace.Basic
import LeanPool.Monlib4.Preq.Ites
/-!
# Direct sum... |
1,997 | lean_file_chunk | 00d448ce39cdb3ec8d8caa435f5041c6ff0f9cfbc4fe950bd8da5177efef51f7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.Eigenspace.Basic
/-!
# Some obvious lemmas on module.End
This file contains some obvious lemmas on `module.End`.
-/
open scoped BigOperato... |
23,944 | lean_file_chunk | c7bc38c45b7466f0be65415d2c2a927bc2ba2a0e959b926a4dab1be7828de307 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.MySpec
import LeanPool.Monlib4.LinearAlgebra.Matrix.Basic
import LeanPool.Monlib4.LinearAlgebra.Matrix.IsAlmostHermitian
import LeanP... |
5,414 | lean_file_chunk | 57293a9f20a514659211a4be077e55b1ebeac2e26fce521c81d662b7678e89ef | lean_source_file | lean_pool_source_file_chunks | theorem _root_.Matrix.coe_diagonal_eq_diagonal_coe {n 𝕜 : Type _} [RCLike 𝕜]
[DecidableEq n] (x : n → ℝ) :
(diagonal (RCLike.ofReal ∘ x) : Matrix n n 𝕜) = CoeTC.coe ∘ diagonal x := by
ext i j
change (if i = j then (x i : 𝕜) else 0) = ((if i = j then x i else 0 : ℝ) : 𝕜)
by_cases h : i = j <;> simp [h... |
7,721 | lean_file_chunk | 2571ed5ee327587a205e63124c386f0c78e4cadabfade7b787990cba5c230aa4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Projection
import Mathlib.LinearAlgebra.TensorProduct.Basic
import Mathlib.Topology.Algebra.StarSubalgebra
... |
7,833 | lean_file_chunk | 93dc684ff7d31e0d7fd501beb5e6eb26c0199457e647b2c34d694f091c652b59 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.Symm
import LeanPool.Monlib4.Preq.RCLikeLe
/-!
# Some obvious basic properties on inner product space
This files provides some ... |
14,270 | lean_file_chunk | 189990167d083d0204f70319018507d0b34da1c28d5e27d00faf0a4af9e5466c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.TensorHilbert
import LeanPool.Monlib4.LinearAlgebra.Ips.Nontracial
import LeanPool.Monlib4.LinearAlgebra.DirectSumFromTo
import Le... |
23,981 | lean_file_chunk | 6b15de64d50eb0e66fa673e37fe46d66182d9c8db407fd84a3558c1fd7eea34b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Matrix.PosEqLinearMapIsPositive
import LeanPool.Monlib4.Preq.RCLikeLe
import LeanPool.Monlib4.LinearAlgebra.IsReal
import LeanPool.Mon... |
9,090 | lean_file_chunk | 5b70a0ca614f4b7af8bad54e3a62b8a38ffc68d46f5953f0d6b22f6b0638efc6 | lean_source_file | lean_pool_source_file_chunks | ∃! α : { x : NNReal // 0 < x }, φ.matrix = (((α : NNReal) : ℝ) : ℂ) • 1 := by
rw [Module.Dual.IsFaithfulPosMap_iff, @and_comm φ.IsPosMap, and_assoc,
Module.Dual.isTracial_pos_map_iff'_of_matrix]
constructor
· rintro ⟨h1, ⟨α, hα, h⟩⟩
have : 0 < (α : ℝ) := by
rw [NNReal.coe_pos, pos_iff_ne_zero]
... |
16,123 | lean_file_chunk | 86765acdfebf99bdd3075f20ab2cac0f53ce9fc01a8ca167c05adb30b5494ab2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.InvariantSubmodule
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Analysis.InnerProductSpace.Spectrum
import LeanPoo... |
23,950 | lean_file_chunk | badbccbc8319d32dff8c722623c7c9a9d67deecea866187db35b120059d314db | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.Functional
import LeanPool.Monlib4.LinearAlgebra.Matrix.PosDefRpow
import LeanPool.Monlib4.LinearAlgebra.MulPrimePrime
import Lean... |
23,966 | lean_file_chunk | fbb85e42a61492bac2bdcf3bf83cf26f8abe29abb7e5b6d478498ee952599b21 | lean_source_file | lean_pool_source_file_chunks | withMatrixInner[φ] (hφ.basis.repr x ij = ⟪hφ.basis ij, x⟫_ℂ) := by
mat_inner_instances φ
rw [hφ.basis_apply, ← hφ.orthonormalBasis_apply, ←
OrthonormalBasis.repr_apply_apply]
rfl
protected theorem toMatrixLinEquiv_symm_apply (hφ : φ.IsFaithfulPosMap) (hψ : ψ.IsFaithfulPosMap)
(x : Matrix (n₂ × n₂) (n × n... |
7,806 | lean_file_chunk | 73cf1bacc6ac6ff5a1a038f7759326380d8eb3bebbf866af7dfea1ebec737493 | lean_source_file | lean_pool_source_file_chunks | PosDef.rpow_mul_rpow, neg_add_cancel, PosDef.rpow_zero, Matrix.mul_one, Matrix.mul_apply,
Matrix.single_eq, kroneckerMap, of_apply, Matrix.one_apply, mul_boole, ite_and,
Finset.sum_ite_eq,
Finset.mem_univ, if_true, eq_comm]
theorem LinearMap.mulRight_toMatrix [hφ : φ.IsFaithfulPosMap] (x : Matrix n n ℂ) ... |
23,983 | lean_file_chunk | 4d9d6b64e3ba70c454d8d073e3d75a57b4e5f6a955c2ca954706f590e05ab17e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.Pos
import LeanPool.Monlib4.LinearAlgebra.Ips.Ips
import LeanPool.Monlib4.LinearAlgebra.Ips.Symm
import LeanPool.Monlib4.RepTheory... |
17,409 | lean_file_chunk | a90bb3bb8057b2b86357ab944cbfc55cfa787f24d26ac6ee0e4031997c720d04 | lean_source_file | lean_pool_source_file_chunks | def ContinuousLinearMap.IsMinimalProjection [InnerProductSpace 𝕜 E] [CompleteSpace E]
(x : E →L[𝕜] E) (U : Submodule 𝕜 E) : Prop :=
IsSelfAdjoint x ∧ Module.finrank 𝕜 U = 1 ∧ LinearMap.IsProj U x
/-- definition of orthogonal projection being minimal
i.e., when the dimension of its space equals one -/
def o... |
4,919 | lean_file_chunk | d8f72c97754adbfc6e4669dab9ff7210e71e634692e7608dfd1548123dd524b1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Opposite
import Mathlib.LinearAlgebra.FiniteDimensional.Basic
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.InnerProductSpace.... |
23,944 | lean_file_chunk | e381e9a855481aca828e9a1bd88e79ecee379e1c30c9dae25f83d5cc08009ce8 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.MulPrimePrime
import LeanPool.Monlib4.LinearAlgebra.Matrix.PosDefRpow
import LeanPool.Monlib4.LinearAlgebra.InnerAut
import LeanPool.M... |
19,481 | lean_file_chunk | 35f63c8f4d6ad26b67db6d96cf4d06708832815b6920c5c39024fe224df3784e | lean_source_file | lean_pool_source_file_chunks | ((op ℂ).toLinearMap : PiMat ℂ k s →ₗ[ℂ] (PiMat ℂ k s)ᵐᵒᵖ)
(star (Module.Dual.pi.IsFaithfulPosMap.sig hψ r b))) := by
let : ∀ i, StarModule ℂ (Matrix ((fun i : k => s i) i) ((fun i : k => s i) i) ℂ) := by
intro i
infer_instance
simp_rw [Module.Dual.pi.IsFaithfulPosMap.psiToFun', LinearMap.coe_mk,
... |
2,988 | lean_file_chunk | e7dddf291ea1808afb3dbbe7aebbb2f5ceb135c90e687cfc9b12f2801ba56cea | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.TensorProduct.Basic
import Mathlib.Algebra.Algebra.Basic
import Mathlib.Data.Opposite
import Mathlib.Algebra.Star.Basic
import LeanPool.Monlib4... |
22,993 | lean_file_chunk | 1aeb93fe5113346c1cc1414aebf79be5064dcf95c01fd2ad515677121ebb6023 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Analysis.InnerProductSpace.Spectrum
import LeanPool.Monlib4.LinearAlgebra.InvariantSubmodule
import LeanPoo... |
23,965 | lean_file_chunk | 4d9022dac1fb9fef7614381a5ddfdbd48458378613b0990cc19883c41a33e4c6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
import LeanPool.Monlib4.LinearAlgebra.Ips.Basic
import LeanPool.Monlib4.LinearAlgebra.IsProjPrime
/-!
# rank one operato... |
4,063 | lean_file_chunk | e978e5b9c4d4f327f5d1d49fd8877095ced171c2a365f0f326037cbc370617fd | lean_source_file | lean_pool_source_file_chunks | (x : E₁) (y : E₂) (r₁ r₂ : 𝕜) :
(rankOne 𝕜 (r₁ • x) (star r₂ • y)).toLinearMap =
(r₁ * r₂) • ((rankOne 𝕜 x y : _ →L[𝕜] _).toLinearMap) :=
by rw [rankOne_smul_smul, ContinuousLinearMap.toLinearMap_smul]
theorem _root_.rankOne_lm_sum_sum {𝕜 E₁ E₂ : Type _} [RCLike 𝕜] [NormedAddCommGroup E₁]
[NormedAd... |
6,500 | lean_file_chunk | d4f514aab6944ade9141c480b141182b6a92e0a789d94f8fdb7896f6ec04369c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.TensorProduct.Associator
import Mathlib.Algebra.Algebra.Bilinear
/-!
# Strict tensor product (wip)
-/
variable {R E F G : Type _} [CommSemir... |
1,604 | lean_file_chunk | ad1a314b40c977172b49879141811ae4214291da4bd8b196dc77ba08bf81932e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.Symmetric
import Mathlib.Analysis.InnerProductSpace.Adjoint
/-!
# some obvious lemmas on self-adjoint operators
This file provi... |
8,593 | lean_file_chunk | dcc6e23b52f40f09a794a2a655a35f05eaf96cf2bb7b18a74beafec65dcb8e54 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.TensorProduct
import Mathlib.LinearAlgebra.FiniteDimensional.Defs
/-!
# Tensor product of inner product spaces
Compatibility le... |
3,906 | lean_file_chunk | 7c337de655764f5c4e9cca2d9637ed50fc73535611dbc8324449ebc1f0cd763e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.InvariantSubmodule
import LeanPool.Monlib4.LinearAlgebra.Ips.Basic
import LeanPool.Monlib4.LinearAlgebra.Ips.Ips
import Mathlib.Analys... |
1,003 | lean_file_chunk | e966a2b3de3a969d3715d40574deb4c1b7a6547264c3ade98fdbebb0367f6369 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.Basic
import LeanPool.Monlib4.LinearAlgebra.Ips.Frob
import LeanPool.Monlib4.LinearAlgebra.Ips.Functional
import LeanPool.Monlib4.... |
3,210 | lean_file_chunk | 453fc45a64aed0006c675cc77bd16380c0e0c89b202f77bc722483114b73d578 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.Projection.Submodule
/-!
# is_proj'
This file contains the definition of `linear_map.is_proj'` and lemmas relating to it, whic... |
8,709 | lean_file_chunk | 5ae513bac87ff9b6799b8a2dd632064a09cae76cc807945f0fb2c75a8e8da9a4 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Basic
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.Algebra.Algebra.Spectrum.Basic
import Mathlib.Algebra.Star.BigOperators
import ... |
6,564 | lean_file_chunk | f301045e2c0823e7ed98fbff3440b6042895561da596a0eb70d304e432f61d6c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.RingTheory.MatrixAlgebra
import Mathlib.LinearAlgebra.TensorProduct.Matrix
import Mathlib.LinearAlgebra.TensorProduct.Finiteness
import LeanPool.Monlib4.Line... |
2,167 | lean_file_chunk | f6edec4e3c456315bcfb25d565af2f70dfc1ea0f12ea820958d9a7746bb32a62 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Opposites
import Mathlib.Algebra.Module.LinearMap.Basic
import Mathlib.Data.Opposite
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Algebra.Alge... |
9,385 | lean_file_chunk | b8f2b5d193c3329dadad86e50fef214a69ebd31d99e155ab39365d6f43d947a1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Bilinear
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.BasicLemmas
import LeanPool.Monlib4.LinearAlgebra.LinearMapOp
/-!
# lmul and rm... |
17,595 | lean_file_chunk | 2e1af29b06054098956284d6798fdfcecc4b254ad97e087918becabd5b5de103 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.TensorProduct.Matrix
import Mathlib.LinearAlgebra.Trace
import Mathlib.LinearAlgebra.Matrix.Hermitian... |
1,134 | lean_file_chunk | 0c05011f087e944d856e4061c0bd8b13cc11c5ce755ce15e6f28ece72e9d06fb | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Matrix.Basic
/-!
# LeanPool.Monlib4.LinearAlgebra.Matrix.Cast
Imported Lean Pool material for `LeanPool.Monlib4.LinearAlgebra.Matrix.Cast`.
-/
variab... |
2,456 | lean_file_chunk | af925b28812c085f3cd83871957de085bf8267ae91b437cd958b689eb68d9e8f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Matrix.Basic
import Mathlib.LinearAlgebra.Matrix.Hermitian
import LeanPool.Monlib4.Preq.Ites
/-!
# Conjugate of a matrix
This file defines the conjug... |
23,985 | lean_file_chunk | 3207269268431c06edcde0ebb33b0eea3fb37d4d913677822cd576cfadde2ede | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.Trace
import Mathlib.Data.Matrix.Basis
import LeanPool.Monlib4.Preq.Dite
import Mathlib.Linear... |
5,524 | lean_file_chunk | 42e0c9e6090771ffda9436446dcb5c9e759bda4f51f6cd76a72fb390ca6308c2 | lean_source_file | lean_pool_source_file_chunks | rw [← blockDiagonal'_mul]
rfl
namespace IsBlockDiagonal
theorem star {R : Type _} [CommSemiring R] [StarAddMonoid R] {k : Type _}
[DecidableEq k] {s : k → Type _} {x : Matrix (Σ i, s i) (Σ i, s i) R} (hx : x.IsBlockDiagonal) :
xᴴ.IsBlockDiagonal := by
rw [IsBlockDiagonal]
nth_rw 2 [← hx.eq]
simp... |
7,251 | lean_file_chunk | 8a3043926b6594394df5f96c1ef51d4abde533c1dbf51f7669707e8e8148839b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.Hermitian
import Mathlib.LinearAlgebra.Matrix.Kronecker
impo... |
689 | lean_file_chunk | 59a1dd88ebddef86c07b7b679158e4e5b6a7af522c962f021e460f085d8ba495 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Matrix.Basic
/-!
# LeanPool.Monlib4.LinearAlgebra.Matrix.PiMat
Imported Lean Pool material for `LeanPool.Monlib4.LinearAlgebra.Matrix.PiMat`.
-/
/--... |
9,409 | lean_file_chunk | d9107cba348aee0f7f53a9a37cf74ed61468745200aa93c70ed5d97074129618 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Matrix.PosEqLinearMapIsPositive
import LeanPool.Monlib4.LinearAlgebra.InnerAut
import LeanPool.Monlib4.LinearAlgebra.Matrix.StarOrder... |
21,494 | lean_file_chunk | 959cb71373316baa2f1845c0b4ce0676246ccd6d3eda7a7e5678a98b601bb471 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.Positive
import Mathlib.Analysis.Matrix.Order
import Mathlib.Analysis.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Nonsingula... |
1,451 | lean_file_chunk | ba57ff9d70d0c25779f371e5899ff6de308f394c79cc3de880f40cdc71717306 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Matrix.Conj
/-!
# Reshaping matrices
This defines the identification between `Mₙₓₘ(R)` and `Rⁿˣᵐ` (see `matrix.reshape`),
and shows... |
6,345 | lean_file_chunk | 38324f2ff336cacc2d3a930a464f1409f533a43a970ead38cb47a7f66785e21e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.Matrix.Spectrum
import LeanPool.Monlib4.LinearAlgebra.Matrix.Basic
import LeanPool.Monlib4.LinearAlgebra.Matrix.IsAlmostHermitian
import LeanPool.Mo... |
13,329 | lean_file_chunk | 7c8fcd1f001a5d06200845bcb58cfa9be3ac3602d94e68292a594f813b395a04 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.PiStarOrderedRing
import LeanPool.Monlib4.LinearAlgebra.PiDirectSum
import LeanPool.Monlib4.LinearAlgebra.InnerAut
import LeanPool.Mo... |
850 | lean_file_chunk | 82e68d3dd196db0cc9a286c8b2f60737627fd1bed0ee816a3b8c0aef8f6a1367 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Matrix.Basic
import LeanPool.Monlib4.LinearAlgebra.Matrix.Cast
import LeanPool.Monlib4.LinearAlgebra.Matrix.Conj
import LeanPool.Monl... |
6,154 | lean_file_chunk | 39579f4fd595ebf057aa22ead4d3fc67b06e6667ea0540c0754fdbaa6495e8e0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Bilinear
import LeanPool.Monlib4.LinearAlgebra.KroneckerToTensor
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.BasicLemmas
import LeanP... |
11,258 | lean_file_chunk | a48291354c2841d16e9247387d5a277eb9da30f3c6af83fc585e2b743a2d1515 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.LinearAlgebra.TensorProduct.Basis
import Mathlib.RingTheory.TensorProd... |
1,895 | lean_file_chunk | 046d55f480fc0ab2dcab4961fb6870c1013033474d10f7ae340edb79a8ba856f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.End
/-!
# One lemma of the spectrum of a linear map
This file just proves that the spectrum of a linear map is commutative.
-/
t... |
2,228 | lean_file_chunk | 52b6eba59c079b74a05ed3568fa98d6523b4db40a7919a16dab8159d2c86900a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Analysis.Normed.Lp.PiLp
import Mathlib.Analysis.InnerProductSpace.Basic
/-!
# Normed additive commutative groups... |
23,975 | lean_file_chunk | 43ea83fe2f1ef3515b7239fd25f28fb07f2377116c7438d1a2285319ca3ebdf7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.Basic
import LeanPool.Monlib4.LinearAlgebra.Ips.Ips
import LeanPool.Monlib4.LinearAlgebra.Ips.RankOne
import LeanPool.Monlib4.Pre... |
8,181 | lean_file_chunk | ea12caa1bf9c089e2869e895853c639bd02fa877987cab8dcbeb4af2c2020d84 | lean_source_file | lean_pool_source_file_chunks | theorem mem_extremePoints_of_closedBall_iff_norm_eq_one
{𝕜 H : Type _} [RCLike 𝕜] [NormedAddCommGroup H] [InnerProductSpace 𝕜 H] [Nontrivial H] (x : H) :
x ∈ Set.extremePoints 𝕜 (Metric.closedBall (0 : H) 1) ↔ ‖x‖ = 1 := by
refine ⟨fun hx => norm_one_of_mem_extremePoints_of_closed_unitBall hx, fun hx => ?_⟩
... |
15,462 | lean_file_chunk | 28d9bbc75c6d176fc88aec53c7e486e84039d22e85007a30353ce4fdb76b701b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Fintype.Prod
import Mathlib.RingTheory.TensorProduct.Basic
import LeanP... |
4,587 | lean_file_chunk | 4e4cc17b589e1f4d741b0d2d0fdc5379fdbf3a6db8d8d9e5be8d360774a2ebb1 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Data.Fintype.Pi
import Mathlib.Algebra.Star.Pi
import Mathlib.Data.Comple... |
23,956 | lean_file_chunk | 283f7d26aac73662d301c5da5022522aea80af71826b901c102bfc66c5cc443e | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.InnerAut
import LeanPool.Monlib4.LinearAlgebra.Matrix.IncludeBlock
import LeanPool.Monlib4.LinearAlgebra.InvariantSubmodule
import Le... |
23,030 | lean_file_chunk | 836a30f5d5e4eefa84f09f0cc2df1e28e94c5d0237d4288cf5b8fa67436c0638 | lean_source_file | lean_pool_source_file_chunks | selfAdjointDecompositionRight_isSelfAdjoint]
intro x hx
obtain ⟨a, b, rfl⟩ := hdec hx
simp only [star_sub, star_mul, star_star, map_sub]
rw [IsSelfAdjoint.of_nonneg (hφ (star_mul_self_nonneg a)),
IsSelfAdjoint.of_nonneg (hφ (star_mul_self_nonneg b))]
omit [Fintype n] [DecidableEq n] in
/-- if a map preserv... |
23,918 | lean_file_chunk | 52e08c98627d84da5638b942210d239baf028fa0183f0c4edd2f238760e87183 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Analysis.InnerProductSpace.Orthonormal
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Analy... |
20,536 | lean_file_chunk | 2b48eb8360a595cb4bbd3a6fbca9ee1ae772fc1705df12d91bbc73bfd6f16ff3 | lean_source_file | lean_pool_source_file_chunks | simp_rw [inner_conj_symm, mul_comm, ← TensorProduct.inner_tmul, ← inner_sum, h,
Coalgebra.comul_eq_mul_adjoint, LinearMap.adjoint_inner_right, mul'_apply,
QuantumSet.inner_conj_left, one_mul, starAlgebra.modAut_star, neg_neg,
modAut_apply_modAut, star_star]
ring_nf
open LinearMap in
lemma _root_.QuantumS... |
1,390 | lean_file_chunk | cbc13edf1df30ff04fa6f717f100c8fff3d11da961a18553904370de094c0f43 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import Mathlib.RingTheory.Coalgebra.Basic
/-!
# LeanPool.Monlib4.LinearAlgebra.QuantumSet.DeltaForm
Imported Lean ... |
23,967 | lean_file_chunk | 0ba5cbe6d1f66803902dc3f8f158876352b47f471eb54ec549a233f68f8663a5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import LeanPool.Monlib4.LinearAlgebra.Ips.MatIps
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Pi
import LeanPool.... |
6,816 | lean_file_chunk | d92b8ec5ba60a1b2b3f3bc3ea9f54b3d9f9a5d4451215ccaaa0d6634d1bd53a7 | lean_source_file | lean_pool_source_file_chunks | letI := Module.Dual.pi.IsFaithfulPosMap.quantumSet (ψ := $ψ)
letI := Module.Dual.PiNormedAddCommGroup (φ := $ψ)
letI := (Module.Dual.PiNormedAddCommGroup (φ :=
$ψ)).toPseudoMetricSpace.toUniformSpace.toTopologicalSpace
letI := (Module.Dual.PiNormedAddCommGroup (φ := $ψ)).toSeminormedAd... |
2,712 | lean_file_chunk | 687441faf64ba5009acaafeab9edc999befc0e3e5074b11182f79794feb9c409 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import LeanPool.Monlib4.LinearAlgebra.MyBimodule
/-!
# The Phi Map
This file packages the upstream `Upsilon` equiv... |
4,394 | lean_file_chunk | e0b092c95c1d6208dc122c7df861559a0ebc67cfcb23a20498287c54e1341002 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.TransferInstance
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
/-!
# Quantum Sets on Finite Products
This file restores the fini... |
23,965 | lean_file_chunk | 4a71248464dc39309aa2e922bdaa2f1cd56b8a3bb8a7525924b36e0bd3cdb36b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
/-!
# LeanPool.Monlib4.LinearAlgebra.QuantumSet.QIso
Imported Lean Pool material for `LeanPool.Monlib4.LinearAlgeb... |
1,051 | lean_file_chunk | 01aff9e87a9f8e1349654a5f34d014b2962c4a954e154b9cac904cdd0126386d | lean_source_file | lean_pool_source_file_chunks | _ = (TensorProduct.comm ℂ _ _).symm.toLinearMap ∘ₗ lT _ Coalgebra.counit := by
rw [LinearMap.adjoint_comp, LinearMap.lTensor_adjoint,
Coalgebra.counit_eq_unit_adjoint, TensorProduct.comm_adjoint]
congr; ext; rfl
/-- for any `qBijective` function `P`,
we get `P ∘ (|1⟩⟨1| ⊗ id) ∘ adjoint P = ... |
18,746 | lean_file_chunk | 338b5633bba48473fd1b00ac6b807b0907a0ee5534bc1721b87ba62aa932a894 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import Mathlib.RingTheory.Coalgebra.Basic
import Mathlib.RingTheory.Coalgebra.Hom
/-!
# Schur Product Operator
Thi... |
2,049 | lean_file_chunk | bbd35effafb61408117e229daf8dc2fd1a41507952faa14fc9bc0ef88cea41b7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.SchurMul
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.TensorProduct
import Mathlib.RingTheory.Coalgebra.TensorProduct
... |
23,979 | lean_file_chunk | 62f45dbc187a7847e186076c65009d0ade89bcf7e4d5910b33f86dac97e4986b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.TensorProduct
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Schu... |
2,190 | lean_file_chunk | 3f1c8062df1212b3d507419b9e46e693a966e05f03e1e968109da0b1cf59f9de | lean_source_file | lean_pool_source_file_chunks | rw [toSubsetAlgEquiv_adjoint, LinearMap.comp_apply]
simp only [AlgEquiv.toLinearMap_apply, map_one]
instance {A : Type*} [hA : PartialOrder A] (r : ℝ) :
PartialOrder (QuantumSet.subset r A) :=
hA
instance (priority := low) {A : Type*} [hA : NonUnitalNonAssocSemiring A] (r : ℝ) :
NonUnitalNonAssocSemiring (Quan... |
18,897 | lean_file_chunk | fbe6d4748130cf3493e3e19f81358e3b2f43c0139011f911a1dcab17d45fac45 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.IsReal
-- import LeanPool.Monlib4.LinearAlgebra.MyIps.Nontracial
import LeanPool.Monlib4.LinearAlgebra.Ips.OpUnop
import LeanPool.Mon... |
10,114 | lean_file_chunk | a19e8c649e0126c93bf201ccf8e270844558eedd45b29e622193680a03091123 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.OrthonormalBasis
/-!
# Tensor Products of Quantum Sets
This fi... |
907 | lean_file_chunk | 679a356d3efa7d97f725e76433953bcd5ab9cc4611a82259cf2112ba095a3627 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Basic
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.DeltaForm
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Instances... |
11,366 | lean_file_chunk | 5892fd0a7d957189054b89812cffb35b3c5f8f619bd23d2aa32098954014de9f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Bilinear
import Mathlib.LinearAlgebra.Basis.VectorSpace
import Mathlib.LinearAlgebra.TensorProduct.Basis
import Mathlib.RingTheory.TensorPro... |
9,993 | lean_file_chunk | 0bb003c26e802b88ff355296cd7a434b504548c1b3886722891eba919cedf7bd | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.TensorProduct.Basis
import Mathlib.LinearAlgebra.FiniteDimensional.Basic
import Mathlib.Analysis.RCLike.Basic
import Mathlib.Algebra.Star.Tenso... |
7,679 | lean_file_chunk | c4df04197b5b2902df83078032d996f573e33fd4b5a2f0fa6438c983380e90fe | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.LinearAlgebra.TensorProduct.Map
import Mathlib.RingTheory.TensorProduct.Maps
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.BasicLemmas
import LeanPool... |
1,040 | lean_file_chunk | 1964debc0f50d9d6074af16e1e5c0dca4767aac873980f6285f44364211b3c74 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.FiniteDimensional
import LeanPool.Monlib4.LinearAlgebra.Ips.TensorHilbert
/-!
# Orthonormal Bases of Tensor Products
... |
18,015 | lean_file_chunk | 16234bdeae08e5ffd7b3e8d78e0126e9dd7b07e46d521df09aec974e61fb8175 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Ips.MinimalProj
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.OrthonormalBasis
import Mathlib.LinearAlgebra.TensorProduct.Finit... |
572 | lean_file_chunk | 0ddf4ee9189c6fce8fbc370b8dac7875acb1f2b2eee42685170d64159df60c3d | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.BasicLemmas
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.FiniteDimensional
import LeanPool.Monlib4.LinearAlgebra... |
13,100 | lean_file_chunk | 0651035660a401018c13794f4ca2989d7ca63dcbf55c2940efb6583c37131c18 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Analysis.InnerProductSpace.PiL2... |
1,379 | lean_file_chunk | e08d851eefa17366566956a96866bab0fbf18369f6ff3a2f58920871fbf61bb7 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Coalgebra
import LeanPool.Monlib4.LinearAlgebra.DirectSumFromTo
import LeanPool.Monlib4.LinearAlgebra.End
import LeanPool.Monlib4.Lin... |
407 | lean_file_chunk | 6967f776e2d19168a2a0a0552df1fbad17df2e590acf5168384b38f3c214f08c | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra
import LeanPool.Monlib4.Other
import LeanPool.Monlib4.Preq
import LeanPool.Monlib4.QuantumGraph
import LeanPool.Monlib4.RepTheory
/-... |
4,497 | lean_file_chunk | e410ffdfa2a0555d528c1dec18dbe5481a3ae817d37d6db1dcda6a1cf41e5190 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2024 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Common
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Mathlib.... |
267 | lean_file_chunk | fe2b73b52edc54b3d0f6447157e53f1b64cb2ff0a0bfd29f193c023cdf697dd5 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.Other.Sonia
/-!
# Other
Import-only index for miscellaneous self-contained monlib4 files.
-/ |
7,944 | lean_file_chunk | 31b464c4fc89302bb4d9f285f5be6b7296bc114a9497a8b60b2b0ba6a13fe984 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Data.Complex.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Data.Complex.BigOperators
/-!
# Some stuff a... |
3,051 | lean_file_chunk | e6caadafd6de3c45c4391236cac398975709b13cd9bd61dea137a342c35d20c3 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Logic.Basic
import Mathlib.Algebra.Group.Defs
import Mathlib.Algebra.Star.Basic
import Mathlib.LinearAlgebra.TensorProduct.Basic
/-!
# Some stuff on dites
... |
827 | lean_file_chunk | 2901b05bfb08cf86c829cf170d83459ceb0eb559a5e31eecef958aa48a524388 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.Matrix.Basic
import Mathlib.Data.Matrix.PEquiv
import Mathlib.LinearAlgebra.UnitaryGroup
/-!
# LeanPool.Monlib4.Preq.Equiv
Imported... |
3,266 | lean_file_chunk | 830f686d2277acf7a52bb964adc351cc026a05129432bda0ea29ae78db44f776 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Group.Defs
import Mathlib.Data.Finset.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Sigma
import Mathlib.Data.Fintype.Prod
/-!
# finset
I... |
1,783 | lean_file_chunk | 64b0cbb42972d7311b82515ca59e895a0d72a0465bf933cc5338a8aa98f72c74 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Star.Basic
import Mathlib.Algebra.Module.LinearMap.Basic
import Mathlib.LinearAlgebra.TensorProduct.Basic
import Mathlib.LinearAlgebra.TensorProduct.... |
1,713 | lean_file_chunk | 7bda6af2ade8571bce7f093e331795051da72f01a094b6a13cea88f106c988e6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Analysis.RCLike.Basic
/-!
# Extra lemmas on RCLike
This file contains extra lemmas on `RCLike`.
-/
namespace RCLike
variable {𝕜 : Type _} [RCLike 𝕜]
... |
384 | lean_file_chunk | 55e2a7babec5ff209212a9de66f0b60bfc2162c0d04e3e795da2c28f3aa91ce0 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.GroupTheory.Subsemigroup.Center
import Mathlib.Algebra.Group.Prod
/-!
# Set center lemmas
`Set.center_prod` and `Set.center_pi` are now in Mathlib; this fi... |
10,256 | lean_file_chunk | 24a79267c16d9b3ec8bb1ded1b9c1c56f66517267b4276a5d80f334fd7134da2 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import Mathlib.Algebra.Star.StarAlgHom
import Mathlib.Algebra.Algebra.Equiv
import Mathlib.LinearAlgebra.Span.Basic
import Mathlib.Algebra.Star.Pi
/-!
# Some stuff on sta... |
519 | lean_file_chunk | ca93a15642e2ebe9b7aa697bf5abd96e6957e71e452035aedb1705fc980ec840 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2026 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.Preq.Complex
import LeanPool.Monlib4.Preq.Dite
import LeanPool.Monlib4.Preq.Equiv
import LeanPool.Monlib4.Preq.Finset
import LeanPool.Monlib4.Preq.... |
23,990 | lean_file_chunk | ca216935b514a23695ee2d7875a46345dbce58f4c6f12ad55a8f231556ab088f | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.SchurMul
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Symm
import LeanPool.Monlib4.LinearAlgebra.TensorProduct.Lemmas
i... |
23,963 | lean_file_chunk | ad591446ce74a119a0e9832312c94b894341104e3099c520af08384643eba500 | lean_source_file | lean_pool_source_file_chunks | ⟨fun h => ⟨h.isIdempotentElem, h.isReal⟩,
fun h => ⟨h.isIdempotentElem, h.isReal⟩⟩
theorem QuantumGraph.Real.toQuantumGraph {f : A →ₗ[ℂ] A} (h : QuantumGraph.Real A f) :
QuantumGraph A f :=
⟨h.isIdempotentElem⟩
theorem quantumGraphReal_iff_Psi_isIdempotentElem_and_isSelfAdjoint {f : A →ₗ[ℂ] A} :
QuantumGraph.Rea... |
1,779 | lean_file_chunk | 8c7e9bbfffa7bae82bb438137217c9e08de248b3f200a254bc4a7f55a32466cf | lean_source_file | lean_pool_source_file_chunks | · have := QuantumSet.starAlgEquiv_commutes_with_modAut_of_isometry' hφ
simp only [gns, gns₂, zero_add, mul_zero] at this ⊢
apply_fun LinearMap.adjoint using LinearEquiv.injective _
simp only [LinearMap.adjoint_comp, LinearMap.adjoint_adjoint, QuantumSet.modAut_adjoint]
exact this
theorem PhiMap.apply_r... |
23,966 | lean_file_chunk | bb1db8407ad0ab038795993560deb3218b6352f4503060db241ca1e0d79de9d6 | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.PhiMap
import LeanPool.Monlib4.QuantumGraph.Basic
import Mathlib.LinearAlgebra.TensorProduct.Opposite
import LeanPool.Monli... |
427 | lean_file_chunk | a42cb303c8dadedc9f00643de6708f7e474f3b28110f1c17d9a210bcd1e07f02 | lean_source_file | lean_pool_source_file_chunks | rw [QuantumSet.normOne_toSubset 0]
exact @QuantumGraph.zero_le_degree_le_norm_one_sq_of_gns
(QuantumSet.subset 0 A) subsetStarAlgebra subsetQuantumSet inferInstance inferInstance
subsetStarOrderedRing
((StarOrderedRing.nonneg_iff_toQuantumSetSubset 0).mp h₁) rfl
(f.toSubsetQuantumSet 0 0)
((Quantu... |
15,731 | lean_file_chunk | 8adb0c6027a47ee42daa8d084ddb9f8872c2ee005c52e99307473598ad1ebf5b | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.QuantumGraph.Basic
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.Pi
import LeanPool.Monlib4.LinearAlgebra.QuantumSet.TensorProduct
import LeanPoo... |
7,754 | lean_file_chunk | ffa574152e50d93dc77fc52e049806419177920dce2754d332dd8ac952c72b4a | lean_source_file | lean_pool_source_file_chunks | /-
Copyright (c) 2023 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
import LeanPool.Monlib4.QuantumGraph.Basic
import LeanPool.Monlib4.QuantumGraph.Degree
/-!
# LeanPool.Monlib4.QuantumGraph.Grad
Imported Lean Pool material for `LeanPool.... |
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