Theorems · Theorem · linear algebra
Matrix.mul_single_apply_same
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {α : Type u_7} [inst : DecidableEq m] [inst_1 : DecidableEq n]
[inst_2 : Fintype m] [inst_3 : NonUnitalNonAssocSemiring α] (c : α) (i : m) (j : n) (a : l) (M : Matrix l m α),
(M * Matrix.single i j c) a j = M a i * c- Defined in
- Mathlib.Data.Matrix.Basis
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.mul_zeroproof · cited by 2,091
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- mul_iteproof · cited by 159
- Matrix.singlestatement · cited by 129
- Finset.sum_ite_eqproof · cited by 85
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.center_eq_scalar_imageproof · cited by 6
- Matrix.mul_transvection_apply_sameproof · cited by 2
- Matrix.col_eq_zero_of_commute_singleproof · cited by 1
- Matrix.diag_eq_of_commute_singleproof · cited by 1
- Matrix.commutator_diag2_transvectionproof · cited by 1
- Matrix.transvection_mem_commutator₁proof · cited by 1
- mulLeftLinearMap_eq_zero_iffproof · cited by 0