Theorems · Theorem · linear algebra
Matrix.separatingRight_iff_forall_mulVec_eq_zero
∀ {m : Type u_1} {n : Type u_2} {R : Type u_3} [inst : CommSemiring R] {M : Matrix m n R} [inst_1 : Finite m]
[inst_2 : Fintype n], M.SeparatingRight ↔ ∀ (v : n → R), M.mulVec v = 0 → v = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFiniteFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finitestatement and proof · cited by 3,029
- one_mulproof · cited by 2,841
- Pi.singleproof · cited by 518
- Matrix.mulVecstatement and proof · cited by 267
- Fintype.ofFiniteproof · cited by 255
- dotProductproof · cited by 194
- Matrix.SeparatingRightstatement · cited by 35
- dotProduct_zeroproof · cited by 11
- single_dotProductproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.SeparatingRight.eq_zero_of_mulVec_eq_zeroproof · cited by 2
- Matrix.nondegenerate_iff_forall_vecMul_and_mulVec_eq_zeroproof · cited by 0