Theorems · Theorem · functional analysis
LinearIsometryEquiv.reflections_generate
∀ {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] [FiniteDimensional ℝ F],
Subgroup.closure (Set.range fun v => (ℝ ∙ v)ᗮ.reflection) = ⊤The orthogonal group of F is generated by reflections.
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- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Set.rangestatement and proof · cited by 4,705
- Subgroupstatement · cited by 3,593
- InnerProductSpacestatement and proof · cited by 3,523
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankproof · cited by 1,770
- Submodule.spanstatement and proof · cited by 1,504
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