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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 0

Determinant of 2x2 matrix

Defined in
Mathlib.LinearAlgebra.Matrix.Determinant.Basic
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.

Matrix.det_fin_two_of · cited by 12Matrix.det_fin_two_ofUpperHalfPlane.denom_ne_zero_of_im · cited by 4UpperHalfPlane.denom_ne_z…isCusp_SL2Z_iff · cited by 3isCusp_SL2Z_iffUpperHalfPlane.moebius_im · cited by 3UpperHalfPlane.moebius_imMatrix.GeneralLinearGroup.IsParabolic.smul_eq_self_iff · cited by 3IsParabolic.smul_eq_self_…UpperHalfPlane.hasStrictDerivAt_smul · cited by 3UpperHalfPlane.hasStrictD…Complex.areaForm · cited by 3Complex.areaFormUpperHalfPlane.tendsto_smul_atImInfty · cited by 2UpperHalfPlane.tendsto_sm…Matrix.SpecialLinearGroup.isCoprime_row · cited by 2SpecialLinearGroup.isCopr…Matrix.IsElliptic.bc_ne_zero · cited by 2IsElliptic.bc_ne_zeroWeierstrassCurve.Affine.CoordinateRing.norm_smul_basis · cited by 2CoordinateRing.norm_smul_…ModularGroup.bottom_row_surj · cited by 2ModularGroup.bottom_row_s…Matrix.SpecialLinearGroup.fin_two_induction · cited by 2SpecialLinearGroup.fin_tw…Matrix.sub_scalar_sq_eq_discr · cited by 2Matrix.sub_scalar_sq_eq_d…ModularGroup.exists_bound_of_invariant_of_isBigO · cited by 2ModularGroup.exists_bound…CommRing · cited by 17173CommRingMatrix · cited by 4303MatrixFinset.univ · cited by 3473Finset.univNat.cast_one · cited by 2501Nat.cast_oneFinset.sum_congr · cited by 2323Finset.sum_congrMatrix.det · cited by 665Matrix.detFinset.sum_singleton · cited by 251Finset.sum_singletonFin.succAbove · cited by 249Fin.succAboveMatrix.submatrix · cited by 183Matrix.submatrixFinset.univ_unique · cited by 94Finset.univ_uniqueFin.sum_univ_succ · cited by 36Fin.sum_univ_succMatrix.det_unique · cited by 15Matrix.det_uniqueMatrix.det_succ_row_zero · cited by 5Matrix.det_succ_row_zeroFin.succ_succAbove_zero · cited by 2Fin.succ_succAbove_zeroMatrix.det_fin_twoCITED BYCITES

Cites14

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Cited by33

Results whose statement or proof uses this declaration.