Theorems · Theorem · linear algebra

LinearMap.BilinForm.separatingRight_toMatrix_iff

∀ {R₂ : Type u_3} {M₂ : Type u_4} [inst : CommRing R₂] [inst_1 : AddCommGroup M₂] [inst_2 : Module R₂ M₂] {ι : Type u_6}
  [inst_3 : DecidableEq ι] [inst_4 : Fintype ι] {B : LinearMap.BilinForm R₂ M₂} (b : Module.Basis ι R₂ M₂),
  ((LinearMap.BilinForm.toMatrix b) B).SeparatingRight ↔ LinearMap.SeparatingRight B

Defined in: Mathlib.LinearAlgebra.Matrix.BilinearForm
Cited by: 1 results in Mathlib
Foundations: Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module DecidableEq Fintype

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement · cited by 62,936
Modulestatement and proof · cited by 20,661
RingHom.idstatement · cited by 18,349
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
LinearMapstatement · cited by 10,215
Fintypestatement and proof · cited by 7,736
Matrixstatement · cited by 4,303
LinearEquivstatement · cited by 3,317
Module.Basisstatement and proof · cited by 1,477
LinearMap.BilinFormstatement and proof · cited by 501
LinearMap.BilinForm.toMatrixstatement · cited by 47

Cited by1

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LinearMap.BilinForm.SeparatingRight.toMatrixproof · cited by 0