Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.det_ne_zero
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] [Nontrivial R]
(g : GL n R), (↑g).det ≠ 0- Cited by
- 13 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- Nontrivialstatement and proof · cited by 2,416
- Units.valstatement · cited by 1,966
- Matrix.detstatement · cited by 665
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- Units.ne_zeroproof · cited by 68
- Matrix.GeneralLinearGroup.detproof · cited by 58
Cited by13
Results whose statement or proof uses this declaration.
- UpperHalfPlane.petersson_slashproof · cited by 3
- UpperHalfPlane.tendsto_smul_atImInftyproof · cited by 2
- Matrix.GeneralLinearGroup.IsParabolic.powproof · cited by 2
- UpperHalfPlane.gl_smul_eq_self_iff_re_eqproof · cited by 1
- UpperHalfPlane.mul_smul'proof · cited by 1
- UpperHalfPlane.smulFDeriv_J_mulproof · cited by 1
- UpperHalfPlane.σ_mulproof · cited by 1
- ModularForm.prod_slash_sum_weightsproof · cited by 1
- MDifferentiable.slashproof · cited by 0
- UpperHalfPlane.det_smulFDerivproof · cited by 0
- UpperHalfPlane.forall_smul_eq_self_iff_mem_centerproof · cited by 0
- Matrix.GeneralLinearGroup.parabolicEigenvalue_ne_zeroproof · cited by 0