Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.upperRightHom_apply
∀ {R : Type u_1} [inst : Ring R] (x : R),
Matrix.GeneralLinearGroup.upperRightHom x =
{ val := !![1, x; 0, 1], inv := !![1, -x; 0, 1], val_inv := ⋯, inv_val := ⋯ }- Cited by
- 8 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Equivstatement · cited by 8,337
- Ringstatement and proof · cited by 7,463
- Matrixstatement · cited by 4,303
- Unitsstatement · cited by 2,804
- Matrix.vecConsstatement · cited by 852
- Matrix.vecEmptystatement · cited by 832
- Matrix.GeneralLinearGroupstatement · cited by 556
- Matrix.ofstatement · cited by 336
- AddCharstatement · cited by 286
- Matrix.GeneralLinearGroup.upperRightHomstatement and proof · cited by 14
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.strictWidthInfty_pos_iffproof · cited by 5
- Subgroup.strictPeriods_eq_zmultiples_one_of_T_memproof · cited by 4
- Subgroup.mem_strictPeriods_iffproof · cited by 3
- SlashInvariantForm.vAdd_apply_of_mem_strictPeriodsproof · cited by 2
- CongruenceSubgroup.strictPeriods_Gammaproof · cited by 2
- Matrix.GeneralLinearGroup.isParabolic_iff_of_upperTriangular_of_detproof · cited by 1
- Matrix.GeneralLinearGroup.injective_upperRightHomproof · cited by 0
- Matrix.GeneralLinearGroup.continuous_upperRightHomproof · cited by 0