Theorems · Theorem · operator theory

LinearMap.IsPositive.ne_zero_iff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {T : E →ₗ[𝕜] E}, T.IsPositive → (T ≠ 0 ↔ ∃ x, 0 < inner 𝕜 (T x) x)

Defined in

Mathlib.Analysis.InnerProductSpace.Positive

Cited by

1 results in Mathlib

Foundations

Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpace