Theorems · Theorem · linear algebra
Matrix.vecMul_vecMul
∀ {m : Type u_2} {n : Type u_3} {o : Type u_4} {α : Type v} [inst : NonUnitalSemiring α] [inst_1 : Fintype n]
[inst_2 : Fintype m] (v : m → α) (M : Matrix m n α) (N : Matrix n o α),
Matrix.vecMul (Matrix.vecMul v M) N = Matrix.vecMul v (M * N)- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 78 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
- NonUnitalSemiringstatement and proof · cited by 339
- Matrix.vecMulstatement · cited by 148
- dotProduct_assocproof · cited by 3
Cited by12
Results whose statement or proof uses this declaration.
- Matrix.PosDef.conjTranspose_mul_mul_sameproof · cited by 3
- Matrix.PosSemidef.conjTranspose_mul_mul_sameproof · cited by 3
- AffineBasis.affineIndependent_of_toMatrix_right_invproof · cited by 1
- Matrix.toLinearMapRight'_mulproof · cited by 1
- AffineBasis.toMatrix_inv_vecMul_toMatrixproof · cited by 1
- Matrix.vecMul_surjective_iff_exists_left_inverseproof · cited by 1
- Matrix.IsHadamard.card_eq_mul_star_of_const_col_sumproof · cited by 1
- Matrix.schur_complement_eq₁₁proof · cited by 1
- Matrix.pow_row_eq_zero_of_leproof · cited by 1
- Matrix.vecMul_mulVecproof · cited by 0
- Matrix.toLinearMapRight'_mul_applyproof · cited by 0
- Matrix.schur_complement_eq₂₂proof · cited by 0