Theorems · Theorem · linear algebra
zero_dotProduct
∀ {m : Type u_2} {α : Type v} [inst : Fintype m] [inst_1 : NonUnitalNonAssocSemiring α] (v : m → α), 0 ⬝ᵥ v = 0- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 9 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.
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
- Finset.univproof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- MulZeroClass.zero_mulproof · cited by 1,625
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Finset.sum_const_zeroproof · cited by 219
- dotProductstatement · cited by 194
Cited by9
Results whose statement or proof uses this declaration.
- Matrix.zero_mulproof · cited by 16
- Matrix.separatingLeft_iff_forall_vecMul_eq_zeroproof · cited by 2
- FirstOrder.Language.presburger.term_realize_eq_add_dotProductproof · cited by 1
- zero_dotProduct'proof · cited by 1
- dotProduct_eq_zeroproof · cited by 1
- dotProduct_eq_zero_iffproof · cited by 1
- LinearIndependent.sum_smul_of_nondegenerateproof · cited by 1
- Matrix.zero_vecMulproof · cited by 1
- not_injective_dotProduct_rightproof · cited by 0