Theorems · Theorem · linear algebra

LinearMap.separatingLeft_congr_iff

∀ {R : Type u_1} {M : Type u_5} {Mₗ₁ : Type u_9} {Mₗ₁' : Type u_10} {Mₗ₂ : Type u_11} {Mₗ₂' : Type u_12}
  [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : AddCommMonoid Mₗ₁]
  [inst_4 : AddCommMonoid Mₗ₂] [inst_5 : AddCommMonoid Mₗ₁'] [inst_6 : AddCommMonoid Mₗ₂'] [inst_7 : Module R Mₗ₁]
  [inst_8 : Module R Mₗ₂] [inst_9 : Module R Mₗ₁'] [inst_10 : Module R Mₗ₂'] {B : Mₗ₁ →ₗ[R] Mₗ₂ →ₗ[R] M}
  (e₁ : Mₗ₁ ≃ₗ[R] Mₗ₁') (e₂ : Mₗ₂ ≃ₗ[R] Mₗ₂'),
  ((e₁.arrowCongr (e₂.arrowCongr (LinearEquiv.refl R M))) B).SeparatingLeft ↔ B.SeparatingLeft

Defined in

Mathlib.LinearAlgebra.SesquilinearForm.Basic

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidAddCommMonoidAddCommMonoidAddCommMonoidModuleModuleModuleModule