Theorems · Theorem · functional analysis

LinearMap.IsSymmetric.adjoint_eq

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [inst_3 : FiniteDimensional 𝕜 E] {A : E →ₗ[𝕜] E}, A.IsSymmetric → LinearMap.adjoint A = A

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

5 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFiniteDimensional