Theorems · Theorem · functional analysis
inner_self_nonneg
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x : E}, 0 ≤ RCLike.re (inner 𝕜 x x)- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- InnerProductSpacestatement and proof · cited by 3,523
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Inner.innerstatement · cited by 1,089
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
- PreInnerProductSpace.Core.re_inner_nonnegproof · cited by 2
- PreInnerProductSpace.toCoreproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- inner_self_eq_norm_mul_normproof · cited by 9
- LinearMap.isPositive_oneproof · cited by 5
- LinearMap.IsIdempotentElem.isPositive_iff_isSymmetricproof · cited by 2
- inner_self_re_eq_normproof · cited by 2
- LinearMap.isPositive_natCastproof · cited by 2
- real_inner_self_nonnegproof · cited by 1