Theorems · Definition · functional analysis

LinearMap.adjoint

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      [inst : RCLike 𝕜] →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : NormedAddCommGroup F] →
            [inst_3 : InnerProductSpace 𝕜 E] →
              [inst_4 : InnerProductSpace 𝕜 F] →
                [FiniteDimensional 𝕜 E] → [FiniteDimensional 𝕜 F] → (E →ₗ[𝕜] F) ≃ₗ⋆[𝕜] F →ₗ[𝕜] E

The adjoint of an operator from the finite-dimensional inner product space E to the finite-dimensional inner product space F.

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

64 results in Mathlib

Foundations

Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupInnerProductSpaceInnerProductSpaceFiniteDimensionalFiniteDimensional