Theorems · Theorem · linear algebra
Matrix.det_fin_two
∀ {R : Type v} [inst : CommRing R] (A : Matrix (Fin 2) (Fin 2) R), A.det = A 0 0 * A 1 1 - A 0 1 * A 1 0Determinant of 2x2 matrix
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- Matrix.detstatement · cited by 665
- Finset.sum_singletonproof · cited by 251
- Fin.succAboveproof · cited by 249
- Matrix.submatrixproof · cited by 183
- Finset.univ_uniqueproof · cited by 94
- Fin.sum_univ_succproof · cited by 36
- Matrix.det_uniqueproof · cited by 15
Cited by33
Results whose statement or proof uses this declaration.
- Matrix.det_fin_two_ofproof · cited by 12
- UpperHalfPlane.denom_ne_zero_of_improof · cited by 4
- isCusp_SL2Z_iffproof · cited by 3
- UpperHalfPlane.moebius_improof · cited by 3
- Matrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iffproof · cited by 3
- UpperHalfPlane.hasStrictDerivAt_smulproof · cited by 3
- Complex.areaFormproof · cited by 3
- UpperHalfPlane.tendsto_smul_atImInftyproof · cited by 2
- Matrix.SpecialLinearGroup.isCoprime_rowproof · cited by 2
- Matrix.IsElliptic.bc_ne_zeroproof · cited by 2
- WeierstrassCurve.Affine.CoordinateRing.norm_smul_basisproof · cited by 2
- ModularGroup.bottom_row_surjproof · cited by 2