Theorems · Theorem · functional analysis
Submodule.map_orthogonal_equiv
∀ {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] (K : Submodule 𝕜 E)
(f : E ≃ₗᵢ[𝕜] F), Submodule.map (↑f.toLinearEquiv) Kᗮ = (Submodule.map (↑f.toLinearEquiv) K)ᗮ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Top.topproof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- LinearMap.rangeproof · cited by 893
- LinearIsometryEquivstatement and proof · cited by 748
- Submodule.mapstatement and proof · cited by 614
- Submodule.orthogonalstatement and proof · cited by 257
- LinearIsometryEquiv.toLinearEquivstatement and proof · cited by 107
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanGeometry.Sphere.orthRadius_mapproof · cited by 0