Theorems · Theorem · linear algebra

IsBaseChange.toDual_apply

∀ {R : Type u_1} [inst : CommSemiring R] {V : Type u_2} [inst_1 : AddCommMonoid V] [inst_2 : Module R V] {W : Type u_3}
  [inst_3 : AddCommMonoid W] [inst_4 : Module R W] {A : Type u_4} [inst_5 : CommSemiring A] [inst_6 : Algebra R A]
  [inst_7 : Module A W] [inst_8 : IsScalarTower R A W] {j : V →ₗ[R] W} (ibc : IsBaseChange A j) (f : Module.Dual R V),
  ibc.toDual f = (Module.Dual.congr ibc.equiv) ((Module.Dual.baseChange A) f)

Defined in

Mathlib.LinearAlgebra.Dual.BaseChange

Cited by

0 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleCommSemiringAlgebraModuleIsScalarTower