Theorems · Theorem · linear algebra
Matrix.transvection_mul_apply_of_ne
∀ {n : Type u_1} {R : Type u₂} [inst : DecidableEq n] [inst_1 : CommRing R] (i j : n) [inst_2 : Fintype n]
{m : Type u_4} (a : n) (b : m), a ≠ i → ∀ (c : R) (M : Matrix n m R), (Matrix.transvection i j c * M) a b = M a b- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 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.
Cites9
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 and proof · cited by 4,303
- add_zeroproof · cited by 2,707
- Matrix.singleproof · cited by 129
- Matrix.one_mulproof · cited by 30
- Matrix.transvectionstatement · cited by 24
- Matrix.add_mulproof · cited by 9
- Matrix.single_mul_apply_of_neproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.Pivot.listTransvecCol_mul_last_row_dropproof · cited by 2
- Matrix.Pivot.listTransvecCol_mul_last_colproof · cited by 1