Theorems · Theorem · linear algebra
Matrix.IsTotallyUnimodular.transpose
∀ {m : Type u_1} {n : Type u_3} {R : Type u_5} [inst : CommRing R] {A : Matrix m n R},
A.IsTotallyUnimodular → A.transpose.IsTotallyUnimodular- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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.
- CommRingstatement and proof · cited by 17,173
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- Matrix.transposestatement and proof · cited by 389
- Matrix.submatrixproof · cited by 183
- Matrix.det.congr_simpproof · cited by 91
- SignType.castproof · cited by 76
- Matrix.det_transposeproof · cited by 51
- Matrix.IsTotallyUnimodularstatement and proof · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.transpose_isTotallyUnimodular_iffproof · cited by 3
- Matrix.emptyCols_isTotallyUnimodularproof · cited by 0