Theorems · Definition · operator theory

LinearMap.IsPositive

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

A linear operator T on a Hilbert space is positive if it is symmetric and ∀ x, 0 ≤ re ⟪T x, x⟫.

Defined in

Mathlib.Analysis.InnerProductSpace.Positive

Cited by

39 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace