Theorems · Theorem · linear algebra
Matrix.separatingLeft_transpose_iff
∀ {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 : Finite n], M.transpose.SeparatingLeft ↔ M.SeparatingRight- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringFiniteFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Fintypeproof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finitestatement and proof · cited by 3,029
- Matrix.transposestatement and proof · cited by 389
- Matrix.mulVecproof · cited by 267
- Fintype.ofFiniteproof · cited by 255
- dotProductproof · cited by 194
- Matrix.SeparatingRightstatement and proof · cited by 35
- Matrix.SeparatingLeftstatement · cited by 33
- Matrix.dotProduct_transpose_mulVecproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.Nondegenerate.of_det_mem_nonZeroDivisorsproof · cited by 3
- Matrix.SeparatingRight.separatingLeft_transposeproof · cited by 0