Theorems · Theorem · functional analysis

InnerProductSpace.rankOne_eq_rankOne_iff_comm

∀ {𝕜 : Type u_4} [inst : RCLike 𝕜] {F : Type u_8} {H : Type u_9} [inst_1 : NormedAddCommGroup F]
  [inst_2 : InnerProductSpace 𝕜 F] [inst_3 : NormedAddCommGroup H] [inst_4 : InnerProductSpace 𝕜 H] {a c : F} {b d : H},
  ((InnerProductSpace.rankOne 𝕜) a) b = ((InnerProductSpace.rankOne 𝕜) c) d ↔
    ((InnerProductSpace.rankOne 𝕜) b) a = ((InnerProductSpace.rankOne 𝕜) d) c

Defined in

Mathlib.Analysis.InnerProductSpace.LinearMap

Cited by

1 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace