Theorems · Definition · linear algebra
LinearEquiv.det
{R : Type u_1} →
[inst : CommRing R] → {M : Type u_2} → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → (M ≃ₗ[R] M) →* RˣOn a LinearEquiv, the domain of LinearMap.det can be promoted to Rˣ.
- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- MonoidHomstatement · cited by 3,629
- LinearEquivstatement · cited by 3,317
- Unitsstatement · cited by 2,804
- MulEquiv.symmproof · cited by 482
- MonoidHom.compproof · cited by 469
- LinearMap.detproof · cited by 127
- MulEquiv.toMonoidHomproof · cited by 126
- Units.mapproof · cited by 95
Cited by52
Results whose statement or proof uses this declaration.
- SpecialLinearGroupproof · cited by 43
- LinearEquiv.coe_detstatement · cited by 11
- Orientation.map_eq_iff_det_posproof · cited by 3
- ZLattice.volume_image_eq_volume_div_covolumeproof · cited by 3
- Module.Basis.map_orientation_eq_det_inv_smulstatement and proof · cited by 3
- Orientation.map_eq_det_inv_smulstatement · cited by 2
- SpecialLinearGroup.mem_center_iffstatement · cited by 2
- ZLattice.covolume_eq_det_invstatement and proof · cited by 1
- Matrix.SpecialLinearGroup.toLin_equiv.toLinearMap_eqstatement · cited by 1
- LinearEquiv.coe_inv_detstatement · cited by 1
- SpecialLinearGroup.centerEquivRootsOfUnity_applystatement · cited by 1
- SpecialLinearGroup.centerEquivRootsOfUnity_apply_applystatement · cited by 1