Theorems · Theorem · linear algebra
Matrix.transvection_mul_transvection_same
∀ {n : Type u_1} {R : Type u₂} [inst : DecidableEq n] [inst_1 : CommRing R] (i j : n) [inst_2 : Fintype n],
i ≠ j → ∀ (c d : R), Matrix.transvection i j c * Matrix.transvection i j d = Matrix.transvection i j (c + d)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqCommRingFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- add_assocproof · cited by 746
- Matrix.singleproof · cited by 129
- Matrix.transvectionstatement · cited by 24
- Matrix.mul_addproof · cited by 11
- Matrix.add_mulproof · cited by 9
- Matrix.single_mul_single_of_neproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.TransvectionStruct.mul_invproof · cited by 2
- Matrix.TransvectionStruct.inv_mulproof · cited by 2