Theorems · Theorem · linear algebra
LinearEquiv.coe_det
∀ {R : Type u_1} [inst : CommRing R] {M : Type u_2} [inst_1 : AddCommGroup M] [inst_2 : Module R M] (f : M ≃ₗ[R] M),
↑(LinearEquiv.det f) = LinearMap.det ↑f- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 127 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.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- MonoidHomstatement · cited by 3,629
- LinearEquivstatement and proof · cited by 3,317
- Unitsstatement · cited by 2,804
- Units.valstatement · cited by 1,966
- LinearEquiv.toLinearMapstatement · cited by 1,171
- LinearMap.detstatement · cited by 127
Cited by11
Results whose statement or proof uses this declaration.
- ZLattice.volume_image_eq_volume_div_covolumeproof · cited by 3
- Orientation.map_eq_iff_det_posproof · cited by 3
- ZLattice.covolume_eq_det_invproof · cited by 1
- LinearEquiv.det_conjproof · cited by 0
- Orientation.map_eq_neg_iff_det_negproof · cited by 0
- Polynomial.det_taylorLinearEquivproof · cited by 0
- Submodule.linearEquiv_det_reflectionproof · cited by 0
- LinearEquiv.transvection.det_eq_oneproof · cited by 0
- linearEquiv_det_rotationproof · cited by 0
- Module.Basis.orientation_comp_linearEquiv_eq_iff_det_posproof · cited by 0
- Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_negproof · cited by 0