Theorems · Definition · linear algebra

Module.Dual.transpose

{R : Type u_1} →
  {M : Type u_3} →
    [inst : CommSemiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {M' : Type u_4} →
            [inst_3 : AddCommMonoid M'] →
              [inst_4 : Module R M'] → (M →ₗ[R] M') →ₗ[R] Module.Dual R M' →ₗ[R] Module.Dual R M

The transposition of linear maps, as a linear map from M →ₗ[R] M' to Dual R M' →ₗ[R] Dual R M.

Defined in

Mathlib.LinearAlgebra.Dual.Defs

Cited by

10 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule