Theorems · Definition · operator theory

LinearMap.IsSymmetric

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] → [inst_1 : SeminormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → (E →ₗ[𝕜] E) → Prop

A (not necessarily bounded) operator on an inner product space is symmetric, if for all x, y, we have ⟪T x, y⟫ = ⟪x, T y⟫.

Defined in

Mathlib.Analysis.InnerProductSpace.Symmetric

Cited by

121 results in Mathlib

Foundations

Depth 46 from the axioms, rests on 492 definitions · uses propext, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpace