Theorems · Theorem · group theory
Matrix.commutator_diag2_transvection
∀ {F : Type u_1} [inst : Field F] (a : F) (ha : a ≠ 0) (b c : F),
c = b * (a ^ 2 - 1) →
⁅Matrix.SpecialLinearGroup.diag2 a ha, Matrix.SpecialLinearGroup.transvection ⋯ b⁆ =
Matrix.SpecialLinearGroup.transvection ⋯ c- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- Bracket.bracketstatement · cited by 642
- mul_negproof · cited by 590
- neg_zeroproof · cited by 542
- Matrix.extproof · cited by 540
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.transvection_mem_commutator₀proof · cited by 1