Theorems · Theorem · linear algebra

LinearMap.apply_toPerfPair_flip

∀ {R : Type u_1} {M : Type u_3} {N : Type u_5} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] [inst_2 : CommRing R]
  [inst_3 : Module R M] [inst_4 : Module R N] (p : M →ₗ[R] N →ₗ[R] R) [inst_5 : p.IsPerfPair] (f : Module.Dual R M)
  (x : M), (p x) (p.flip.toPerfPair.symm f) = f x

Defined in

Mathlib.LinearAlgebra.PerfectPairing.Basic

Cited by

1 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupCommRingModuleModuleLinearMap.IsPerfPair