Theorems · Theorem · linear algebra
dotProduct_comm
∀ {m : Type u_2} {α : Type v} [inst : Fintype m] [inst_1 : AddCommMonoid α] [inst_2 : CommMagma α] (v w : m → α),
v ⬝ᵥ w = w ⬝ᵥ v- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- mul_commproof · cited by 2,262
- dotProductstatement · cited by 194
- CommMagmastatement and proof · cited by 57
Cited by13
Results whose statement or proof uses this declaration.
- Matrix.transpose_mulproof · cited by 14
- Matrix.vecMul_transposeproof · cited by 8
- Matrix.dotProduct_transpose_mulVecproof · cited by 3
- Matrix.mulVec_transposeproof · cited by 3
- Matrix.isPositive_toEuclideanLin_iffproof · cited by 2
- Projectivization.cross_orthogonal_leftproof · cited by 2
- Projectivization.orthogonal_commproof · cited by 2
- InnerProductGeometry.norm_ofLp_crossProductproof · cited by 1
- LDL.diag_eq_lowerInv_conjproof · cited by 1
- Matrix.IsHermitian.im_star_dotProduct_mulVec_selfproof · cited by 1
- Matrix.IsHermitian.eigenvalues_eqproof · cited by 1
- Matrix.charpoly_vecMulVecproof · cited by 0