Theorems · Theorem · functional analysis
norm_sub_eq_norm_add
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{v w : E}, inner 𝕜 v w = 0 → ‖w - v‖ = ‖w + v‖Given two orthogonal vectors, their sum and difference have equal norms.
- Defined in
- Mathlib.Analysis.InnerProductSpace.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement · cited by 25,697
- Norm.normstatement · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- add_zeroproof · cited by 2,707
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- zero_addproof · cited by 2,366
- Inner.innerstatement and proof · cited by 1,089
- map_addproof · cited by 964
- sub_zeroproof · cited by 938
- norm_nonnegproof · cited by 725
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.