Theorems · Theorem · linear algebra
dotProduct_zero
∀ {m : Type u_2} {α : Type v} [inst : Fintype m] [inst_1 : NonUnitalNonAssocSemiring α] (v : m → α), v ⬝ᵥ 0 = 0- Defined in
- Mathlib.Data.Matrix.Mul
- Cited by
- 11 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.mul_zeroproof · cited by 2,091
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Finset.sum_const_zeroproof · cited by 219
- dotProductstatement · cited by 194
Cited by11
Results whose statement or proof uses this declaration.
- Matrix.mul_zeroproof · cited by 14
- Matrix.mulVec_zeroproof · cited by 6
- Matrix.PosDef.isUnitproof · cited by 4
- Matrix.separatingRight_iff_forall_mulVec_eq_zeroproof · cited by 2
- Matrix.ker_mulVecLin_transpose_mul_selfproof · cited by 1
- dotProduct_zero'proof · cited by 1
- Matrix.PosDef.fromBlocks₁₁proof · cited by 1
- Projectivization.exists_not_self_orthogonalproof · cited by 1
- Matrix.PosSemidef.dotProduct_mulVec_zero_iffproof · cited by 1
- Matrix.IsHermitian.eigenvalues_eq_zero_iffproof · cited by 1
- not_injective_dotProduct_leftproof · cited by 0