Theorems · Theorem · linear algebra
Matrix.IsTotallyUnimodular.submatrix
∀ {m : Type u_1} {m' : Type u_2} {n : Type u_3} {n' : Type u_4} {R : Type u_5} [inst : CommRing R] {A : Matrix m n R}
(f : m' → m) (g : n' → n), A.IsTotallyUnimodular → (A.submatrix f g).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.
Cites8
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.submatrixstatement and proof · cited by 183
- Matrix.det.congr_simpproof · cited by 91
- SignType.castproof · cited by 76
- Matrix.submatrix_submatrixproof · cited by 24
- Matrix.IsTotallyUnimodularstatement and proof · cited by 22
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.fromRows_isTotallyUnimodular_iff_rowsproof · cited by 2
- Matrix.IsTotallyUnimodular.reindexproof · cited by 1