Theorems · Theorem · functional analysis
Submodule.linearEquiv_det_reflection
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
(K : Submodule 𝕜 E) [inst_3 : FiniteDimensional 𝕜 ↥K],
LinearEquiv.det K.reflection.toLinearEquiv = (-1) ^ Module.finrank 𝕜 ↥Kᗮ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- MonoidHomstatement · cited by 3,629
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivstatement · cited by 3,317
- RCLikestatement and proof · cited by 2,829
- Unitsstatement · cited by 2,804
- Units.valproof · cited by 1,966
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement and proof · cited by 1,770
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