Theorems · Theorem · operator theory

InnerProductSpace.isPositive_rankOne_self

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  (x : E), (((InnerProductSpace.rankOne 𝕜) x) x).IsPositive

Defined in: Mathlib.Analysis.InnerProductSpace.Positive
Cited by: 1 results in Mathlib
Foundations: Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
RingHom.idstatement · cited by 18,349
NormedAddCommGroupstatement and proof · cited by 15,752
Norm.normproof · cited by 5,413
ContinuousLinearMapstatement · cited by 5,352
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
Inner.innerproof · cited by 1,089
starRingEndstatement · cited by 671
inner_smul_leftproof · cited by 49
ContinuousLinearMap.IsPositivestatement · cited by 38
InnerProductSpace.rankOnestatement and proof · cited by 35

Cited by1

Results whose statement or proof uses this declaration.

ContinuousLinearMap.isPositive_iff_eq_sum_rankOneproof · cited by 1