Theorems · Theorem · functional analysis

Module.Basis.toOrthonormalBasis.congr_simp

∀ {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 v_1 : Module.Basis ι 𝕜 E) (e_v : v = v_1)
  (hv : Orthonormal 𝕜 ⇑v), v.toOrthonormalBasis hv = v_1.toOrthonormalBasis ⋯

Defined in: Mathlib.Analysis.InnerProductSpace.PiL2
Cited by: 0 results in Mathlib
Foundations: Depth 229 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace Fintype

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DFunLike.coestatement and proof · cited by 62,936
NormedAddCommGroupstatement and proof · cited by 15,752
Fintypestatement and proof · cited by 7,736
InnerProductSpacestatement and proof · cited by 3,523
RCLikestatement and proof · cited by 2,829
Module.Basisstatement and proof · cited by 1,477
OrthonormalBasisstatement · cited by 188
Orthonormalstatement and proof · cited by 85
Module.Basis.toOrthonormalBasisstatement and proof · cited by 5

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