Theorems · Theorem · linear algebra
LinearMap.det_id
∀ {M : Type u_2} [inst : AddCommGroup M] {A : Type u_5} [inst_1 : CommRing A] [inst_2 : Module A M],
LinearMap.det LinearMap.id = 1- Defined in
- Mathlib.LinearAlgebra.Determinant
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupCommRingModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · 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
- LinearMap.idstatement · cited by 625
- LinearMap.detstatement and proof · cited by 127
- MonoidHom.map_oneproof · cited by 27
Cited by7
Results whose statement or proof uses this declaration.
- LinearEquiv.det_mul_det_symmproof · cited by 2
- NumberField.mixedEmbedding.det_fderivPolarCoordRealSymmproof · cited by 2
- LinearEquiv.det_symm_mul_detproof · cited by 1
- LinearMap.range_lt_top_of_det_eq_zeroproof · cited by 1
- Matrix.SpecialLinearGroup.lineStab_fix_of_spanproof · cited by 1
- SpecialLinearGroup.subsingleton_of_finrank_eq_oneproof · cited by 0
- LinearEquiv.det_reflproof · cited by 0