Theorems · Theorem · functional analysis

Submodule.IsOrtho.map_iff

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F] (f : E ≃ₗᵢ[𝕜] F)
  {U V : Submodule 𝕜 E}, Submodule.map (↑↑↑f) U ⟂ Submodule.map (↑↑↑f) V ↔ U ⟂ V

Defined in

Mathlib.Analysis.InnerProductSpace.Orthogonal

Cited by

1 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace