Theorems · Theorem · linear algebra

IsBaseChange.transvection

∀ {R : Type u_3} {V : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid V] [inst_2 : Module R V] (A : Type u_5)
  [inst_3 : CommSemiring A] [inst_4 : Algebra R A] {W : Type u_6} [inst_5 : AddCommMonoid W] [inst_6 : Module R W]
  [inst_7 : Module A W] [inst_8 : IsScalarTower R A W] {ε : V →ₗ[R] W} (ibc : IsBaseChange A ε) (f : Module.Dual R V)
  (v : V), ibc.endHom (LinearMap.transvection f v) = LinearMap.transvection (ibc.toDual f) (ε v)

Defined in

Mathlib.LinearAlgebra.Transvection.Basic

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleCommSemiringAlgebraAddCommMonoidModuleModuleIsScalarTower