Theorems · Theorem · linear algebra
Matrix.IsIrreducible.transpose
∀ {n : Type u_1} {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] {A : Matrix n n R},
A.IsIrreducible → A.transpose.IsIrreducibleIrreducibility is invariant under transpose.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- Matrixstatement and proof · cited by 4,303
- Quiverproof · cited by 405
- Matrix.transposestatement and proof · cited by 389
- Quiver.Pathproof · cited by 166
- Quiver.Path.compproof · cited by 45
- Quiver.Path.lengthproof · cited by 39
- Quiver.Hom.toPathproof · cited by 38
- Quiver.Path.casesOnproof · cited by 12
- Matrix.IsIrreduciblestatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.isIrreducible_transpose_iffproof · cited by 0