Theorems · Definition · linear algebra
Matrix.SeparatingLeft
{m : Type u_1} →
{n : Type u_2} → {R : Type u_3} → [NonUnitalNonAssocSemiring R] → [Finite m] → [Finite n] → Matrix m n R → PropA matrix M is right-separating if for all v ≠ 0, there is a w with v * M * w ≠ 0.
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Finitestatement and proof · cited by 3,029
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- Matrix.mulVecproof · cited by 267
- dotProductproof · cited by 194
Cited by35
Results whose statement or proof uses this declaration.
- Matrix.separatingLeft_iff_det_ne_zerostatement · cited by 4
- Matrix.separatingLeft_toLinearMap₂'_iffstatement · cited by 4
- Matrix.Nondegenerate.separatingLeftstatement · cited by 4
- Matrix.separatingLeft_defstatement · cited by 3
- Matrix.separatingLeft_toLinearMap₂_iffstatement and proof · cited by 3
- Matrix.SeparatingLeft.toLinearMap₂'statement and proof · cited by 3
- Matrix.separatingLeft_iff_forall_vecMul_eq_zerostatement · cited by 2
- Matrix.separatingLeft_iff_separatingRightstatement · cited by 2
- Matrix.separatingLeft_transpose_iffstatement · cited by 2
- Matrix.nondegenerate_iffstatement and proof · cited by 2
- Matrix.nondegenerate_iff_separatingLeftstatement and proof · cited by 2
- Matrix.SeparatingLeft.eq_zero_of_vecMul_eq_zerostatement and proof · cited by 2