Theorems · Theorem · functional analysis
Submodule.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],
LinearMap.det ↑K.reflection.toLinearEquiv = (-1) ^ Module.finrank 𝕜 ↥Kᗮ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites61
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 and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Matrixproof · cited by 4,303
- mul_oneproof · cited by 3,885
- MonoidHomstatement · cited by 3,629
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivproof · cited by 3,317
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.linearEquiv_det_reflectionproof · cited by 0