Theorems · Theorem · linear algebra
Matrix.separatingRight_def
∀ {m : Type u_1} {n : Type u_2} {R : Type u_3} [inst : CommSemiring R] {M : Matrix m n R} [inst_1 : Fintype m]
[inst_2 : Fintype n], M.SeparatingRight ↔ ∀ (w : n → R), (∀ (v : m → R), v ⬝ᵥ M.mulVec w = 0) → w = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFintypeFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidproof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- NonUnitalNonAssocSemiringproof · cited by 1,081
- Matrix.mulVecstatement and proof · cited by 267
- Fintype.ofFiniteproof · cited by 255
- dotProductstatement and proof · cited by 194
- Matrix.SeparatingRightstatement · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.separatingRight_toLinearMap₂'_iffproof · cited by 4
- Matrix.nondegenerate_defproof · cited by 3
- Matrix.separatingRight_iff_forall_mulVec_eq_zeroproof · cited by 2