Theorems · Theorem · linear algebra
Matrix.mul_add
∀ {m : Type u_2} {n : Type u_3} {o : Type u_4} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype n]
(L : Matrix m n α) (M N : Matrix n o α), L * (M + N) = L * M + L * N- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.extproof · cited by 540
- dotProduct_addproof · cited by 6
Cited by13
Results whose statement or proof uses this declaration.
- mulLeftLinearMapproof · cited by 9
- Matrix.transvection_mul_transvection_sameproof · cited by 2
- Matrix.addMonoidHomMulLeftproof · cited by 2
- Matrix.mul_transvection_apply_of_neproof · cited by 2
- Matrix.mul_transvection_apply_sameproof · cited by 2
- Matrix.mul_subproof · cited by 1
- Matrix.det_add_mulproof · cited by 0
- CStarMatrix.mul_addproof · cited by 0
- Matrix.add_mul_mul_invOf_mul_eq_oneproof · cited by 0
- Matrix.add_mul_mul_invOf_mul_eq_one'proof · cited by 0
- Matrix.det_add_replicateCol_mul_replicateRowproof · cited by 0
- Matrix.add_mul_mul_mul_invOf_eq_oneproof · cited by 0