Theorems · Theorem · linear algebra

Matrix.vecMul_smul

∀ {m : Type u_2} {n : Type u_3} {R : Type u_7} {α : Type v} [inst : NonUnitalNonAssocSemiring α] [inst_1 : Fintype m]
  [inst_2 : DistribSMul R α] [SMulCommClass R α α] (v : m → α) (b : R) (M : Matrix m n α),
  Matrix.vecMul v (b • M) = b • Matrix.vecMul v M

Defined in: Mathlib.Data.Matrix.Mul
Cited by: 1 results in Mathlib
Foundations: Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NonUnitalNonAssocSemiring Fintype DistribSMul SMulCommClass

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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
SMulCommClassstatement and proof · cited by 1,927
NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
Matrix.vecMulstatement · cited by 148
DistribSMulstatement and proof · cited by 117
dotProduct_smulproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

Matrix.IsHadamard.card_eq_mul_star_of_const_col_sumproof · cited by 1