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Theorems · Theorem · linear algebra

Matrix.one_fromCols_isTotallyUnimodular_iff

∀ {m : Type u_1} {n : Type u_3} {R : Type u_5} [inst : CommRing R] [inst_1 : DecidableEq m] (A : Matrix m n R),
  (Matrix.fromCols 1 A).IsTotallyUnimodular ↔ A.IsTotallyUnimodular
Defined in
Mathlib.LinearAlgebra.Matrix.Determinant.TotallyUnimodular
Cited by
1 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.IsTotallyUnimodular.one_fromCols · cited by 0IsTotallyUnimodular.one_f…CommRing · cited by 17173CommRingMatrix · cited by 4303MatrixMatrix.transpose · cited by 389Matrix.transposeMatrix.fromRows · cited by 35Matrix.fromRowsMatrix.fromCols · cited by 30Matrix.fromColsMatrix.transpose_one · cited by 22Matrix.transpose_oneMatrix.IsTotallyUnimodular · cited by 22Matrix.IsTotallyUnimodularMatrix.transpose_fromCols · cited by 3Matrix.transpose_fromColsMatrix.transpose_isTotallyUnimodular_iff · cited by 3Matrix.transpose_isTotall…Matrix.one_fromRows_isTotallyUnimodular_iff · cited by 2Matrix.one_fromRows_isTot…Matrix.one_fromCols_isTotally…CITED BYCITES

Cites10

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Cited by1

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