Theorems · Theorem · functional analysis
InnerProductSpace.gramSchmidt_mem_span
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{ι : Type u_3} [inst_3 : LinearOrder ι] [inst_4 : LocallyFiniteOrderBot ι] [inst_5 : WellFoundedLT ι] (f : ι → E)
{j i : ι}, i ≤ j → InnerProductSpace.gramSchmidt 𝕜 f i ∈ Submodule.span 𝕜 (f '' Set.Iic j)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 187 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.
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearOrderstatement and proof · cited by 8,572
- Submodulestatement · cited by 7,192
- Set.imagestatement · cited by 5,609
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Submodule.spanstatement · cited by 1,504
- Set.Iicstatement · cited by 1,111
- WellFoundedLTstatement and proof · cited by 491
- LocallyFiniteOrderBotstatement and proof · cited by 286
- InnerProductSpace.gramSchmidtstatement · cited by 30
Cited by4
Results whose statement or proof uses this declaration.
- InnerProductSpace.span_gramSchmidt_Iioproof · cited by 2
- InnerProductSpace.gramSchmidt_of_orthogonalproof · cited by 1
- InnerProductSpace.span_gramSchmidtproof · cited by 0
- InnerProductSpace.span_gramSchmidt_Iicproof · cited by 0