Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.val_det_apply
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (A : GL n R),
↑(Matrix.GeneralLinearGroup.det A) = (↑A).det- Cited by
- 31 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
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 and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Matrix.detstatement · cited by 665
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- Matrix.GeneralLinearGroup.detstatement and proof · cited by 58
Cited by31
Results whose statement or proof uses this declaration.
- UpperHalfPlane.denom_ne_zero_of_improof · cited by 4
- UpperHalfPlane.det_Jproof · cited by 3
- UpperHalfPlane.moebius_improof · cited by 3
- Matrix.GeneralLinearGroup.det_scalarproof · cited by 3
- UpperHalfPlane.gl_smul_eq_self_iff_quadraticproof · cited by 2
- UpperHalfPlane.coe_J_smulproof · cited by 2
- SlashInvariantForm.vAdd_apply_of_mem_strictPeriodsproof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_dist_sq_eqproof · cited by 1
- UpperHalfPlane.IsZeroAtImInfty.slashproof · cited by 1
- UpperHalfPlane.gl_smul_eq_self_iff_re_eqproof · cited by 1
- UpperHalfPlane.isElliptic_of_exists_smul_eq_selfproof · cited by 1
- Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_detproof · cited by 1