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 |
|---|---|---|---|---|---|
2,503 | lean_file_chunk | 3a42179fa66ed2863980b0c43dc307d82a8c4b05544483d6168464e5440710c7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.LinearAlgebra.Matrix.PosDef
/-!
# Sesquilinear forms over a star ring
This file provides some properties about sesquilinear forms `M →... |
23,982 | lean_file_chunk | 6d2fdeb5e960374902136195432fdd570676dd1d55be1224d796a5814b0ac168 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Andreas Swerdlow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andreas Swerdlow
-/
module
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib.LinearAlgebra.BilinearMap
public import Mathlib.LinearAlgebra.LinearIndependent.Lemm... |
15,492 | lean_file_chunk | 2b85bc426cfb2f7e6ed9f76dc4e013a9d1be2bea40336db8c7f7a4e9a6e8f71c | lean_source_file | pkg_mathlib_source_file_chunks | def SeparatingRight (B : M₁ →ₛₗ[I₁] M₂ →ₛₗ[I₂] M) : Prop :=
∀ y : M₂, (∀ x : M₁, B x y = 0) → y = 0
/-- A bilinear map is called non-degenerate if it is left-separating and right-separating. -/
def Nondegenerate (B : M₁ →ₛₗ[I₁] M₂ →ₛₗ[I₂] M) : Prop :=
SeparatingLeft B ∧ SeparatingRight B
section Linear
variable ... |
6,611 | lean_file_chunk | 5e978668a29169034bdd46e59058b09ddbafac37a55e36e1f449a8a443cc8ab1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.TensorAlgebra.Basic
public import Mathlib.LinearAlgebra.TensorPower.Basic
/-!
# Tensor algebras as direct sums of tensor powers... |
13,004 | lean_file_chunk | c0068d8cf45281b8d0bc0927039f1b394b2fb41e44a48331bbb8f6788e76872c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Adam Topaz
-/
module
public import Mathlib.Algebra.FreeAlgebra
public import Mathlib.Algebra.RingQuot
public import Mathlib.Algebra.TrivSqZeroExt.Basic
public import Mathlib.Algebra.Algeb... |
2,403 | lean_file_chunk | a3e9254eae7b091c5288b027898c7d6d4d2270f25baa09a6409669ff607ec217 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.TensorAlgebra.Basic
public import Mathlib.RingTheory.GradedAlgebra.Basic
/-!
# Results about the grading structure of the tenso... |
3,302 | lean_file_chunk | 845ede105388367af39d3eb46f50171bd8b706b042fcc467e132ae33ce561cc4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.TensorAlgebra.Basic
public import Mathlib.LinearAlgebra.FreeAlgebra
/-!
# A basis for `TensorAlgebra R M`
## Main definitions
... |
13,005 | lean_file_chunk | 8eea8ecfa0a4424e84c10df13e0b449ac2129b9f9baf2379e002e5be866b0279 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.LinearAlgebra.PerfectPairing.Basic
public import Mathlib.LinearAlgebra.Matrix.Basis
public import Mathlib.LinearAlgebra.Matrix.BaseChange
/-!... |
9,653 | lean_file_chunk | 47eed5bce938902a068ebd2c42e5b0c8a510eed31bc6c0df9dbd13d306404600 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Yaël Dillies
-/
module
public import Mathlib.LinearAlgebra.Dual.Lemmas
/-!
# Perfect pairings
This file defines perfect pairings of modules.
A perfect pairing of two (lef... |
23,971 | lean_file_chunk | 3bc96aa701f05b2965208629ae14d2d120260af82bd4a190fd77dae7579a911f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Filippo A. E. Nuccio. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Filippo A. E. Nuccio, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
public import Mathlib.LinearAlgebra.Matrix.Trace
public import Mathlib.R... |
878 | lean_file_chunk | 0d01e4166d263aca58c833b40287810c214dbaff56f8f7b1ff660d6c849e5eb1 | lean_source_file | pkg_mathlib_source_file_chunks | kroneckerMapBilinear_mul_mul (TensorProduct.mk R α β) tmul_mul_tmul A B A' B'
end Semiring
section CommRing
variable [CommRing R] [CommRing α] [CommRing β] [Algebra R α] [Algebra R β]
unseal mul in
theorem det_kroneckerTMul [Fintype m] [Fintype n] [DecidableEq m] [DecidableEq n]
(A : Matrix m m α) (B : Matrix n... |
16,884 | lean_file_chunk | 85ebe68cb372110aed90e6e2b50ba823f53c3032a5748b37fec965e78946ac35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
module
public import Mathlib.Algebra.Star.BigOperators
public import Mathlib.Algebra.Star.Module
publ... |
23,980 | lean_file_chunk | 20f9cac704fac52bd91abb0d8447b9ec20a24e2363afb38b778fd0945723d15f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Lu-Ming Zhang
-/
module
public import Mathlib.Data.Matrix.Invertible
public import Mathlib.LinearAlgebra.FiniteDimensional.Basic
public import Mathlib.LinearAlgebra.Matrix.A... |
7,300 | lean_file_chunk | 8a3467bc6b5184d5f23aa6fa022b9b227fc83bed8fc7a61fb14c70b9351f35da | lean_source_file | pkg_mathlib_source_file_chunks | (A + U * C * V)⁻¹ = A⁻¹ - A⁻¹ * U * C * (C + C * V * A⁻¹ * U * C)⁻¹ * C * V * A⁻¹ := by
obtain ⟨_⟩ := hA.nonempty_invertible
obtain ⟨ih⟩ := h.nonempty_invertible
simp only [← invOf_eq_nonsing_inv] at ih
letI := invertibleAddMulMul' A U C V
simp only [← invOf_eq_nonsing_inv]
apply invOf_add_mul_mul'
end Woo... |
6,002 | lean_file_chunk | b7dd4a22c864f0ba6e88ebf6c14079355f4b80aa58c183db4e214afadf8e3a54 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
module
public import Mathlib.LinearAlgebra.Matrix.Kronecker
public import Mathlib.LinearAlgebra.Matrix.Orthogonal
public import Mathlib.LinearAlgebra.Matrix.Symmetric
... |
7,045 | lean_file_chunk | c82a2c6e90083b2632c7a44729748baf86e8b8c07eacddfa69fa539c650b5e85 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
module
public import Mathlib.Algebra.Group.Fin.Basic
public import Mathlib.LinearAlgebra.Matrix.Symmetric
public import Mathlib.Tactic.Abel
/-!
# Circulant matrices
... |
4,603 | lean_file_chunk | 647ac3afd806ca37959079c7103a5d687974f99ef068e533bf65ce8fa25795a5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Judith Ludwig, Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Judith Ludwig, Christian Merten
-/
module
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
public import Mathlib.LinearAlgebra.Matrix.Permutation
pu... |
17,650 | lean_file_chunk | 99beb938e2ff6c357900f10903910945b54627ae27caf13ad31d7174c4cf4ba1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
/-!
# Row and column matrices
This file provides results about row and column matrices.
## ... |
289 | lean_file_chunk | 0e6ad1df40a84d6f3a62bc157e5f84325f8d9b78511fad4177637a6490de8e00 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Algebra.Order.Algebra
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
public import Mathlib.Data.Sym.Sym2
public import Mathlib.Tactic.NormNum.GCD
public import Mathlib.Tactic.Positivity
deprecated_module (since := "2025-11-18") |
3,060 | lean_file_chunk | 98e5ac33844c4cb243a4211f6f1f207276dacc3d5ac80906716d74d53a51c386 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.Dimension.LinearMap
public import Mathlib.LinearAlgebra.Matrix.ToLin
/-!
# Diag... |
23,963 | lean_file_chunk | 601e608e6ae4d0cd27b488dfa11db57de584e288722e26d17e202b1a4d824141 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Mohanad Ahmed
-/
module
public import Mathlib.Algebra.CharP.Invertible
public import Mathlib.Algebra.Order.Ring.Star
public import Mathlib.Data.Real.Star
publi... |
1,427 | lean_file_chunk | d77bf644d9dd123010578f84c029d4a072b483f21609ad46658ab5815a9d1e58 | lean_source_file | pkg_mathlib_source_file_chunks | rw [dotProduct_mulVec, ← Sum.elim_comp_inl_inr x, schur_complement_eq₁₁ B D _ _ hA.1]
apply le_add_of_nonneg_of_le
· rw [← dotProduct_mulVec]
apply (posSemidef_iff_dotProduct_mulVec.mp hA.posSemidef).2
· rw [← dotProduct_mulVec (star (x ∘ Sum.inr))]
apply (posSemidef_iff_dotProduct_mulVec.mp h).... |
3,896 | lean_file_chunk | 9be212da06468b42ff3a49baf5a7a2aeb5e077518e262ccdc13794756b09ff35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yunzhou Xie
-/
module
public import Mathlib.Algebra.Module.BigOperators
public import Mathlib.Data.Matrix.Basis
/-!
# Mₙ(R)-module structure on `Mⁿ`
## Main Results
- `Matrix.Module.m... |
21,446 | lean_file_chunk | e82be21c0af4834bffd728fb4aba80f264cf03c3d8a68e923b07551a010005aa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying
-/
module
public import Mathlib.LinearAlgebra.BilinearForm.Properties
public import Mathlib.LinearAlgebra.Matrix.SesquilinearForm
/-!
# Bilinear form
This file... |
4,999 | lean_file_chunk | d8b97d8e1fe74cf841cedafc4b85f8ba0fd412d0236056eff265c81444db18a7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
public import Mathlib.LinearAlgebra.Matrix.Adjugate
/-!
# Matr... |
6,153 | lean_file_chunk | 6e526e2787683fb18815f03427bc40f89b6e8239d84b0e710f6e0c7f81c55980 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
module
public import Mathlib.LinearAlgebra.Matrix.Trace
public import Mathlib.Data.Matrix.Basic
/-!
# Hadamard product of matrices
This file defines the Hadamard pro... |
23,987 | lean_file_chunk | e06deaca5664b943b84358376302e1a3114bc5231c1df8e53a21f74e6c8ed3a5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Kexing Ying, Moritz Doll
-/
module
public import Mathlib.Algebra.GroupWithZero.Action.Opposite
public import Mathlib.LinearAlgebra.Finsupp.VectorSpace
public import Mathlib.... |
11,532 | lean_file_chunk | 8d62d5a7c73e22c544fe21da8d15eaf145cb1bec54d7b40572a3e9fcfc1a1ae1 | lean_source_file | pkg_mathlib_source_file_chunks | B = B' ↔ LinearMap.toMatrix₂ b₁ b₂ B = LinearMap.toMatrix₂ b₁ b₂ B' := by
intro B B'
constructor <;> intro h
· rw [h]
· exact (LinearMap.toMatrix₂ b₁ b₂).injective h
simp_rw [h, LinearMap.toMatrix₂_comp b₂ b₂, LinearMap.toMatrix₂_compl₂ b₁ b₁,
LinearMap.toMatrix_toLin, LinearMap.toMatrix₂_toLinear... |
20,570 | lean_file_chunk | 7923e18276e4d7a5da47deddaf5d33a16a3afe4a3699b816775d66dc0579345e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Determinant
public import Mathlib.LinearAlgebra.Dimension.OrzechProperty
public import Mathlib.LinearAlgebra.... |
4,071 | lean_file_chunk | 9a78d2dad23317334ca44aa1117f7393a16cd2c0ba2383d7f35074244dd54b4c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Analysis.CStarAlgebra.Matrix
public import Mathlib.Data.Matrix.PEquiv
public import Mathlib.Data.Set.Card
public import Mathlib.LinearAlgebra.... |
5,094 | lean_file_chunk | 4a31f0bcc801f17e0d43713b9dc6f0d2286721d26920d9b8e56a3e58fe8601cf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.Algebra.GCDMonoid.Finset
public import Mathlib.Algebra.GCDMonoid.Nat
public import Mathlib.Da... |
763 | lean_file_chunk | ed4f58b055bfcf04c148aef0003bd6ca420c0dfda105462dcbd9fcd4869a3040 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
module
public import Mathlib.Algebra.CharP.Defs
public import Mathlib.Data.Matrix.Diagonal
/-!
# Matrices in prime characteristic
In this file we prove that matric... |
10,804 | lean_file_chunk | c24132351d0c3ef595d90e220a1c881550d1ec8170357964f4a03db6e20f84ba | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
public import Mathlib.LinearAlgebra.Matrix.Symmetric
/-!
# Integer powers of square matrices
... |
5,308 | lean_file_chunk | 583ab606119395684c292f882f207fd528313cf9d590fecbedf5e34a49d22433 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
/-!
# Changing the index type of a matrix
This file c... |
21,522 | lean_file_chunk | 8025851501378511854847bfb4b88077ba2fd45aa0ed72dcd8aab7e303612277 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Eric Wieser, Jeremy Avigad, Johan Commelin
-/
module
public import Mathlib.Data.Matrix.Invertible
public import Mathlib.LinearAlgebra.Matrix.NonsingularInverse... |
23,997 | lean_file_chunk | e4db09d35f060fd6a0f173f68c82b4669e71b68dfb9849f08a27686ffc4521f4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.Algebra.Algebra.Subalgebra.Tower
public import Mathlib.Algebra.Module.Projective
public import... |
23,938 | lean_file_chunk | 8537a414ae2eb52c432276e6501427e8b0e9ca3ff803b9c4766cceba52bec188 | lean_source_file | pkg_mathlib_source_file_chunks | theorem LinearMap.toMatrix_apply' (f : M₁ →ₗ[R] M₂) (i : m) (j : n) :
LinearMap.toMatrix v₁ v₂ f i j = v₂.repr (f (v₁ j)) i :=
LinearMap.toMatrix_apply v₁ v₂ f i j
theorem LinearMap.toMatrix_transpose_apply' (f : M₁ →ₗ[R] M₂) (j : n) :
(LinearMap.toMatrix v₁ v₂ f)ᵀ j = v₂.repr (f (v₁ j)) :=
LinearMap.toMat... |
1,897 | lean_file_chunk | 8497e0c00809a0fe2ca3da74a8775aeec9fe7eeded34834706976a3756806d18 | lean_source_file | pkg_mathlib_source_file_chunks | (.mapMatrix <| .moduleEndSelf _) <| .symm <| endVecAlgEquivMatrixEnd ..
/-- A matrix ring is isomorphic to the opposite of an endomorphism ring. -/
def matrixRingEquivEndVecMulOpposite : Matrix ι ι A ≃+* (Module.End A (ι → A))ᵐᵒᵖ :=
(matrixAlgEquivEndVecMulOpposite ℕ).toRingEquiv
theorem isStablyFiniteRing_iff_isDe... |
11,738 | lean_file_chunk | 29dfbe0e464dd77a9caa027691878c18b8e0bec91d103cc7424fae110a7e8d3a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Wojciech Nawrocki
-/
module
public import Mathlib.Data.Matrix.Basis
public import Mathlib.GroupTheory.Congruence.BigOperators
public import Mathlib.RingTheory.Ideal.Lattic... |
1,739 | lean_file_chunk | b03d1d496efd476c55de40dc0cec14a7925e0dd88e53ed529f81a356006db03e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yunzhou Xie. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yunzhou Xie
-/
module
public import Mathlib.Data.Matrix.Basic
/-!
# One by one matrices
This file proves that one by one matrices over a base are equivalent to the base itself under th... |
10,550 | lean_file_chunk | 2da6f4de82ff2a062336b92cd3571d8ac843794a9ee48f5b32c83ee8fe1ff9bd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Steven Herbert. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Steven Herbert
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.Data.Matrix.Mul
public import Mathlib.Analysis.Convex.Basic
public import Mathlib.LinearAlgebra.... |
11,551 | lean_file_chunk | fdcfdf0f580b26b60b354e6a9b81341748071e1c0294a1d3e019518577856844 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Browning. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Browning
-/
module
public import Mathlib.Algebra.Group.Embedding
public import Mathlib.Data.Matrix.Mul
public import Mathlib.GroupTheory.Perm.Sign
import Mathlib.Algebra.Modu... |
17,542 | lean_file_chunk | 610de14c15759c07b8536c179c9dcf3395fd3b7c46c229e5a3f5f4c274570842 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Eric Wieser
-/
module
public import Mathlib.Algebra.Group.Fin.Tuple
public import Mathlib.Data.Fin.VecNotation
public import Mathlib.LinearAlgebra.Matrix.RowCol
public impor... |
21,578 | lean_file_chunk | 61decbe36494f7e0416dde43e9c1f4e3094957fd925fe6aab5db33ce8b654da1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Ellen Arlt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ellen Arlt, Blair Shi, Sean Leather, Mario Carneiro, Johan Commelin, Lu-Ming Zhang
-/
module
public import Mathlib.Algebra.Module.Pi
public import Mathlib.Logic.Nontrivial.Basic
/-!
# Ma... |
8,590 | lean_file_chunk | 8ce866843d168ddb791da69b2f17bcb5e3ad522abe4bfb1fb63e3bc544e9038e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.Data.Matrix.Basis
public import Mathlib.Data.Matrix.Block
public import Mathlib.LinearAlgebra.... |
15,618 | lean_file_chunk | 272c41b71fbac660c548e6f2c7fb648a181d3cfb6275239db86f27630878585f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen, Wen Yang
-/
module
public import Mathlib.LinearAlgebra.Matrix.Transvection
public import Mathlib.LinearAlgebra.Matrix.Nonsing... |
2,820 | lean_file_chunk | ba7c83bd07e351fa7f5bdce5ceff640ceedde15421e2805b4b51f13808f3580a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.MvPolynomial.CommRing
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
/-... |
7,262 | lean_file_chunk | 8f022bde2945c16d435c9f6677820da8c1e5f1531191f9aae2e17bbaa2e15326 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Matrix.Hadamard
public import Mathlib.LinearAlgebra.Matrix.Kronecker
public import Mathlib.LinearAlgebra.Matrix.Trace
/-! # Vec... |
23,939 | lean_file_chunk | f5a0c65ff743d35464d59c58e160ed8d8943986a52ff9d79d494af9cbf0cf608 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Data.Matrix.Basis
public import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
public import Mathlib.LinearAlgebra.Matrix.Reindex
... |
9,317 | lean_file_chunk | e78edf44e37ef6627bc3a5606612615243191d0f9111b41f787b82b538ec493d | lean_source_file | pkg_mathlib_source_file_chunks | -- we have already proved this when the last coefficient is nonzero
by_cases hM : M (inr unit) (inr unit) = 0; swap
· exact exists_isTwoBlockDiagonal_of_ne_zero M hM
-- when the last coefficient is zero but there is a nonzero coefficient on the last row or the
-- last column, we will first put this nonzero coef... |
11,030 | lean_file_chunk | 9d0c5cab46dba891f0ac04900649cb788038782d655d6e272d78e13061b5e5bd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Chris Birkbeck. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Birkbeck
-/
module
public import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
public import Mathlib.Data.Int.Interval
/-!
# Matrices with fixed determinant
This file define... |
6,716 | lean_file_chunk | 002d28b203e1665438b3fbb7a2913b5f4809c440598c0a66df523071754c7d84 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.Algebra.Order.Star.Basic
public import Mathlib.Algebra.Star.Pi
public import Mathlib.LinearAlg... |
2,032 | lean_file_chunk | 4e15bcf2123b6380c68a3f5c2e31ee75e2bda139dd3b99528a221e9a80e57aee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
module
public import Mathlib.Data.Matrix.Mul
/-!
# Orthogonal
This file contains definitions and properties concerning orthogonality of rows and columns.
## Main re... |
974 | lean_file_chunk | 4d95a4644d20025b3005a711225baa14ee4f7ed8e94b77d771b004e5056864c0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Wen Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Wen Yang
-/
module
public import Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup
/-!
# Projective Special Linear Group
## Notation
In the `MatrixGroups` locale:
* `PSL(n, R)` is a short... |
21,393 | lean_file_chunk | 5088e6d29ca7839a92293c79f303b24402d0980c276de4d7b5d9c1a02305d3d3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Algebra.Regular.Basic
public import Mathlib.LinearAlgebra.Matrix.Symmetric
public import Mathlib.LinearAlgebra.Matrix.MvPolynomial
public impo... |
4,304 | lean_file_chunk | e5360de8b64e1b9117d31145647a32b197d15779892567a019eba5d49c38061b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Moritz Firsching. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Firsching
-/
module
public import Mathlib.Data.Fintype.Perm
public import Mathlib.LinearAlgebra.Matrix.RowCol
/-!
# Permanent of a matrix
This file defines the permanent of ... |
2,008 | lean_file_chunk | 47472ac8ede4ea0275f5c8dd603960cb3844b9f76aeefc30639292b0b8f928b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.Data.Matrix.Basis
public import Mathlib.LinearAlgebra.StdBasis
/-!
# Standard basis on matric... |
4,819 | lean_file_chunk | db698cb008aa6457c7bd85599958ba08560ae7a47d30a87ad8db5aeb0fb82084 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Algebra.Module.Projective
public import Mathlib.LinearAlgebra.Matrix.ToLin
public import Mathlib.LinearAlgebra.Matrix.SemiringInverse
public... |
1,925 | lean_file_chunk | 9a9e89babbf909067a6cf29a3a82e97b885b26bed889a7d9e263cf385e38108b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.DFinsupp
public import Mathlib.LinearAlgebra.Dual.Basis
public import Mathlib.Li... |
3,549 | lean_file_chunk | 8cf7366150228614594c02006e03a22ad8520a3256d9f04d9f644ae5aa29d21f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.Polynomial.BigOperators
public import Mathlib.Algebra.Polynomial.Degree.Lemmas
public import Mathlib.LinearAlgebra.Matrix.Dete... |
227 | lean_file_chunk | 12fc5afdbf1d54da5aadd87fba40659bf7d8887048cc78cdda5b609094710bff | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.SpecialFunctions.Bernstein
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
public import Mathlib.Tactic.NormNum.GCD
deprecated_module (since := "2025-11-13") |
18,649 | lean_file_chunk | 4ceb4ffd79bdc1b56eecc40eaad67d1c8635faa0c7ecd46fa32448861fc811a5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Wen Yang
-/
module
public import Mathlib.Data.Fintype.Parity
public import Mathlib.LinearAlgebra.Matrix.Adjugate
public import Mathlib.LinearAlgebra.Matrix.ToLin
public impo... |
5,983 | lean_file_chunk | 503087debe1fde67505a8132c78af5419d2f01a5d3f111ea258194b6b6e3719d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Lu-Ming Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lu-Ming Zhang
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.Data.Matrix.Block
/-!
# Symmetric matrices
This file contains the definition and basic results a... |
10,669 | lean_file_chunk | 7c26ee1aab5f06e3f3ff5609c2f8a5dcc2f66bf3c2a72528cd91096f7d917077 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.Basis.Submodule
public import Mathlib.LinearAlgebra.Matrix.Reindex
public import... |
2,333 | lean_file_chunk | 07ff535fd8cf22d768a0f52523ca7c9f16fef29055a17b7f0af482065a556c25 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
module
public import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
public import Mathlib.Algebra.Field.Subfield.Defs
/-!
# Matrices and base change
This file is a home... |
15,330 | lean_file_chunk | 82e9abf14b047e90a471da06b880d691b9e3d929e8ce27cccb707f679ed5a307 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Alexander Bentkamp. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp
-/
module
public import Mathlib.Algebra.Star.Pi
public import Mathlib.LinearAlgebra.Matrix.Hadamard
public import Mathlib.LinearAlgebra.Matrix.ZPow
/-! # Hermi... |
3,544 | lean_file_chunk | 665909e30e18b227c4b29ce4b62c20b0602dc5ce04233581c55d46e60ba445c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Xavier Roblot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Xavier Roblot
-/
module
public import Mathlib.Analysis.Normed.Field.Basic
public import Mathlib.LinearAlgebra.Eigenspace.Basic
public import Mathlib.LinearAlgebra.Determinant
/-!
# Ge... |
1,899 | lean_file_chunk | 598dad6962fb91b10891749b7053955fd5ea3a806cea240008e677ac5838df0a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.LinearAlgebra.FiniteDimensional.Defs
public import Mat... |
2,851 | lean_file_chunk | 66ef1e5bb71499fb24bc4e7f46cc85c5a46dd266f4b2d8840df0f823c59890d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public import Mathlib.Algebra.Order.BigOperators.Ring.Finset
public import Mathlib.Data.Int.AbsoluteValue
public import Mathlib.LinearAlgebra.Matrix.Determinant.Bas... |
6,242 | lean_file_chunk | 78bffa5c67af185a8d1200fd3722e288c56e1c5d856c0e0787254eb7cdeb9469 | lean_source_file | pkg_mathlib_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
-/
module
public import Mathlib.Algebra.Star.LinearMap
public import Mathlib.Algebra.Star.StarAlgHom
public import Mathlib.Algebra.WithConv
public import Mathlib.LinearAlgebr... |
10,339 | lean_file_chunk | e0dbeffb91236193754df83f9b2764c35cb24a620a50b22fbb6011d5072aec22 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Patrick Massot, Casper Putz, Anne Baanen
-/
module
public import Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup.Defs
public import Mathlib.LinearAlgebra.Matrix.Nondeg... |
5,263 | lean_file_chunk | c55d1100bbceeab25126c6dc987d96138333b84241b75e577e800044c71bcd36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.Algebra.Algebra.Defs
public import Mathlib.LinearAlgebra.Basis.Basic
/-!
# Bases and scalar multipl... |
3,669 | lean_file_chunk | c11af9503b8f12f5fb02d2953c407a69818097784696eaa6290a73fdf035849b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib.LinearAlgebra.Pi
/-!
# Bases indexed by `Fin`
-/
@... |
2,394 | lean_file_chunk | 43ac6fd13c70f0eea12f0393b1294bdb630903e9ebfd5a1358437c9e97991a91 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
module
public import Mathlib.LinearAlgebra.BilinearMap
public import Mathlib.LinearAlgebra.Basis.Defs
/-!
# Lemmas about bilinear maps with a basis over each argument
-/
... |
2,131 | lean_file_chunk | 067af90d5ac7efc58395e559a70bb2daf7263c73e7861c31125ef18c351b5565 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.LinearAlgebra.FiniteDimensional.Defs
/-!
# Basis of an opposite space
This file defines the basis of an opposite space and shows
that the op... |
4,220 | lean_file_chunk | 03695615de4b7b1e93a8aafa4c60344651af201bd4ed4b46addebffd23db1918 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot
-/
module
public import Mathlib.Data.Fin.FlagRange
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib.LinearAlgebra.Dual.Basis
publ... |
3,643 | lean_file_chunk | efe1d96fe330342ca393000a4d3be5a160b1cf6ff6fd8de2ae2df63a0ff39a24 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.LinearAlgebra.Prod
public import Mathlib.LinearAlgebra.Basis.Defs
public import Mathlib.LinearAlgebr... |
16,195 | lean_file_chunk | f9d47747cf972c911adbe782ba03ecde82ac85dbefc15960d08a380551862d19 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.LinearAlgebra.FreeModule.Basic
public import Mathlib.LinearAlgebra.LinearIndependent.Lemmas
public i... |
11,890 | lean_file_chunk | 5ed7b59325829ebb655e34327d19c0ca04b007d053219cde3e616cf72dc100fc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.LinearAlgebra.Basis.Defs
public import Mathlib.LinearAlgebra.LinearIndependent.Basic
public import M... |
6,406 | lean_file_chunk | 2fe23f1ae24ee882e7e44e8e8b92b67a446bbaec836ceb2ad69785441215572c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp, Kim Morrison
-/
module
public import Mathlib.LinearAlgebra.Basis.Defs
public import Mathlib.LinearAlgebra.LinearIndependent.Defs
pu... |
23,976 | lean_file_chunk | f9c71f48172d8a3b1b5af4f5340246d2c86ba8046d506bb32ea83cdea097d003 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.LinearAlgebra.Finsupp.LinearCombination
/-!
# Bases
This file defines bases in a module or vector ... |
1,846 | lean_file_chunk | 1e505560d424fc7116b744728edb0b6aa859f42fb1e8d00ec441cd256d8427e7 | lean_source_file | pkg_mathlib_source_file_chunks | theorem coe_sumCoords : (b.sumCoords : M → R) = fun m => (b.repr m).sum fun _ => id :=
rfl
@[simp high]
theorem coe_sumCoords_of_fintype [Fintype ι] : (b.sumCoords : M → R) = ∑ i, b.coord i := by
ext m
simp only [sumCoords, Finsupp.sum_fintype, LinearMap.id_coe, LinearEquiv.coe_coe, coord_apply,
id, Fintype.... |
6,754 | lean_file_chunk | a42087e004311a1c519599bd1f5bbcd530a6664f757ce8bf7de3475ad595f7a4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Christian Merten. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Christian Merten
-/
module
public import Mathlib.Algebra.Exact
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib.LinearAlgebra.Projection
/-!
# Basis from a spl... |
8,849 | lean_file_chunk | b994b043b4c7acdbbcaa8f2c5b3d0ebad832bcc51e46bb23d0a0fe6d1752d6ff | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Alexander Bentkamp
-/
module
public import Mathlib.Algebra.Algebra.Basic
public import Mathlib.LinearAlgebra.Basis.Basic
/-!
# Bases of submodules
-/
... |
22,319 | lean_file_chunk | 976af4b97b341645a92fcac4633a4954f8ada95b935734a4c5704576d7a2808b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison
-/
module
public import Mathlib.LinearAlgebra.Dimension.Constructions
public import Mathlib.LinearAlgebra.Dimension.StrongR... |
6,054 | lean_file_chunk | b9319386200ba2ffcff6a17a117f1bf7a1e5bdeb8d084f7e40ccb1977efb52fd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes, Anne Baanen
-/
module
public import Mathlib.SetTheory.Cardinal.ToNat
public import Mathlib.LinearAlgebra.Dimension.Basic
/-!
# Finite dimension of vector spaces
Definiti... |
23,982 | lean_file_chunk | 64d179b3ef9c7d12b5848bc34abf14648a6bd52d6e195e726b9e8a254ca0e5c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib.LinearAlgebra.Basis.Submodule
public import Mathlib.LinearAlgebra.Dimension.Finrank
public i... |
7,260 | lean_file_chunk | 6c906061515ecba810ec03be9e3ed66a8bb492fcce186e18f5d23b03ae1819a6 | lean_source_file | pkg_mathlib_source_file_chunks | rw [← not_subsingleton_iff_nontrivial, ← iff_not_comm]
simp [Module.finrank_eq_zero_iff_of_free]
/-- If `M` is finite, then `finrank N = rank N` for all `N : Submodule M`. Note that
such an `N` need not be finitely generated. -/
protected theorem _root_.Submodule.finrank_eq_rank [Module.Finite R M] (N : Submodule R ... |
22,754 | lean_file_chunk | 731441baf07caf6887a87e7e6f8b773ada2ae64a48e858ba51c619909a560783 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison
-/
module
public import Mathlib.Algebra.Algebra.Tower
public import Mathlib.LinearAlgebra.Basis.Basic
public import Mathlib... |
23,962 | lean_file_chunk | dcfd70f1e219a29edcea46247324f83318c6be8b1991496b46a66c6e5480206f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen, Kim Morrison, Chris Hughes, Anne Baanen
-/
module
public import Mathlib.Algebra.Algebra.Subalgebra.Lattice
public import Mathlib.LinearA... |
584 | lean_file_chunk | 5c5733332ffe6fc05c8f8249588cd362e324df86b4bb8d5c4c45ac1c50699300 | lean_source_file | pkg_mathlib_source_file_chunks | simp only [← Module.Basis.coord_apply]
rw [← LinearMap.comp_apply]
revert v
rw [← LinearMap.ext_iff]
apply (sumQuot bW bQ).ext
intro x
induction x with
| inl i =>
simp [sumQuot_inl, LinearMap.comp_apply,
(Quotient.mk_eq_zero W).mpr (Submodule.coe_mem (bW i))]
| inr i =>
classical
simp ... |
3,658 | lean_file_chunk | 08a25adda76b90565b8a7c5499b28df5f5c7144b998d5078964ba9eeaf9a392a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl, Sander Dahmen,
Kim Morrison, Chris Hughes, Anne Baanen, Junyan Xu
-/
module
public import Mathlib.LinearAlgebra.Basis.VectorSpace
public import Mathlib... |
10,096 | lean_file_chunk | dff3cc178be159e6cc764f2777801f36119dfded952e779c72ddb0b3913babf3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Algebra.Module.LocalizedModule.Submodule
public import Mathlib.LinearAlgebra.Dimension.DivisionRing
public import Mathlib.RingTheory.IsTensorP... |
5,072 | lean_file_chunk | 2c9b894fe7970c52626d11fb84fb169ce7e7959d4f8af3a227439b8ca12e081a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
module
public import Mathlib.Algebra.Module.Projective
public import Mathlib.LinearAlgebra.Dimension.DivisionRing
public import Mathlib.LinearAlgebra.Dimension.FreeA... |
12,215 | lean_file_chunk | 0bcc3d3c596b5ac3d159b782184d91c306dc2eb5520782a3b6c02b9d0d91bf0f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.Dimension.Constructions
public import Mathlib.LinearAlgebra.Dimension.Finite
public import Mathlib.LinearAlgebra.Isomorphisms
pu... |
870 | lean_file_chunk | f38624f6b9c8a81283db5fef05968155bc73ad10a91a9d651e043605853da832 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Kim Morrison, Eric Wieser, Junyan Xu, Andrew Yang
-/
module
public import Mathlib.LinearAlgebra.Dimension.Basic
/-!
# Dimension of trivial modules
-/
public section
vari... |
4,037 | lean_file_chunk | bd6123aae3fcb4313ef1963e2b1aa6f97498045fcb16111435bd5bf992d81740 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Junyan Xu
-/
module
public import Mathlib.LinearAlgebra.Dimension.Finite
public import Mathlib.RingTheory.Noetherian.Orzech
/-! # Bases of modules and the Orzech property
... |
16,109 | lean_file_chunk | d96664bc73ef743d124db51641eae8179b6bfdd87be85e30ab34faaa6f915731 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca
-/
module
public import Mathlib.LinearAlgebra.Dimension.StrongRankCondition
public import Mathlib.LinearAlgebra.FreeModule.Finite.Basic
public import Mathlib.RingTheo... |
12,400 | lean_file_chunk | a9969572b7b4001aa846184fbc94d548ce50c9833507fead236af3492b5d6c1b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jz Pan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jz Pan
-/
module
public import Mathlib.LinearAlgebra.Dimension.Constructions
public import Mathlib.LinearAlgebra.Dimension.Subsingleton
/-!
# Some results on free modules over rings satisfy... |
6,286 | lean_file_chunk | 8c6f2cd12d44e200c08475a5fda65f6cbb2341922a21416d7993bcc0cb43b356 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
module
public import Mathlib.Algebra.Field.Opposite
public import Mathlib.LinearAlgebra.Basis.VectorSpace
public import Mathlib.LinearAlgebra.Dimension.Constructions
public im... |
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