Theorems · Theorem · functional analysis

InnerProductSpace.toMatrix_rankOne

∀ {𝕜 : Type u_7} {E : Type u_8} {F : Type u_9} {ι : Type u_10} {ι' : Type u_11} [inst : RCLike 𝕜]
  [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F]
  [inst_4 : InnerProductSpace 𝕜 F] [inst_5 : Finite ι] [inst_6 : Fintype ι'] [inst_7 : DecidableEq ι'] (x : E) (y : F)
  (b : Module.Basis ι 𝕜 E) (b' : OrthonormalBasis ι' 𝕜 F),
  (LinearMap.toMatrix b'.toBasis b) ↑(((InnerProductSpace.rankOne 𝕜) x) y) =
    Matrix.vecMulVec (⇑(b.repr x)) (star (b'.repr y).ofLp)

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

0 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupNormedSpaceNormedAddCommGroupInnerProductSpaceFiniteFintypeDecidableEq