Theorems · Definition · linear algebra

LinearMap.IsAdjointPair

{R : Type u_1} →
  {M : Type u_5} →
    {M₁ : Type u_6} →
      {M₃ : Type u_8} →
        [inst : CommSemiring R] →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : Module R M] →
              [inst_3 : AddCommMonoid M₁] →
                [inst_4 : Module R M₁] →
                  [inst_5 : AddCommMonoid M₃] →
                    [inst_6 : Module R M₃] →
                      {I : R →+* R} → (M →ₗ[R] M →ₛₗ[I] M₃) → (M₁ →ₗ[R] M₁ →ₛₗ[I] M₃) → (M → M₁) → (M₁ → M) → Prop

Given a pair of modules equipped with bilinear maps, this is the condition for a pair of maps between them to be mutually adjoint.

Defined in

Mathlib.LinearAlgebra.SesquilinearForm.Basic

Cited by

20 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleAddCommMonoidModule