Theorems · Theorem · functional analysis

OrthonormalBasis.coe_mk

∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι] {v : ι → E} (hon : Orthonormal 𝕜 v)
  (hsp : ⊤ ≤ Submodule.span 𝕜 (Set.range v)), ⇑(OrthonormalBasis.mk hon hsp) = v

Defined in: Mathlib.Analysis.InnerProductSpace.PiL2
Cited by: 3 results in Mathlib
Foundations: Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace Fintype

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Cites15

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
NormedAddCommGroupstatement and proof · cited by 15,752
Top.topstatement and proof · cited by 9,680
Fintypestatement and proof · cited by 7,736
Submodulestatement · cited by 7,192
Set.rangestatement and proof · cited by 4,705
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
Submodule.spanstatement and proof · cited by 1,504
OrthonormalBasisstatement and proof · cited by 188
Orthonormalstatement and proof · cited by 85
Module.Basis.coe_mkproof · cited by 33

Cited by3

Results whose statement or proof uses this declaration.

OrthonormalBasis.coe_of_orthogonal_eq_bot_mkproof · cited by 1
HilbertBasis.coe_toOrthonormalBasisproof · cited by 0
OrthonormalBasis.span_applyproof · cited by 0