Theorems · Theorem · linear algebra
Matrix.single_vecMul
∀ {m : Type u_2} {n : Type u_3} {R : Type u_7} [inst : Fintype m] [inst_1 : DecidableEq m]
[inst_2 : NonUnitalNonAssocSemiring R] (M : Matrix m n R) (i : m) (x : R),
Matrix.vecMul (Pi.single i x) M = x • M.row i- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Pi.singlestatement · cited by 518
- Matrix.vecMulstatement · cited by 148
- Matrix.rowstatement · cited by 40
- single_dotProductproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.single_one_vecMulproof · cited by 2
- CStarMatrix.toCLM_apply_singleproof · cited by 2
- Matrix.vecMul_injectiveproof · cited by 1
- Matrix.single_mul_eq_updateRow_zeroproof · cited by 0