Theorems · Theorem · linear algebra
LinearMap.coe_det
∀ {M : Type u_2} [inst : AddCommGroup M] {A : Type u_5} [inst_1 : CommRing A] [inst_2 : Module A M]
[inst_3 : DecidableEq M],
⇑LinearMap.det = ⇑(if H : ∃ s, Nonempty (Module.Basis (↥s) A M) then LinearMap.detAux (Trunc.mk ⋯.some) else 1)- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Fintypeproof · cited by 7,736
- MonoidHomstatement and proof · cited by 3,629
- Module.Basisstatement and proof · cited by 1,477
- DFunLikeproof · cited by 576
- Nonempty.somestatement and proof · cited by 340
Cited by6
Results whose statement or proof uses this declaration.
- LinearMap.det_conjproof · cited by 5
- LinearMap.det_smulproof · cited by 5
- LinearMap.finite_of_det_ne_oneproof · cited by 2
- LinearMap.det_eq_det_toMatrix_of_finsetproof · cited by 2
- Module.Free.of_det_ne_oneproof · cited by 1
- LinearMap.free_of_det_ne_oneproof · cited by 0