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Theorems · Theorem · linear algebra

Matrix.IsIrreducible.connected

∀ {n : Type u_1} {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] {A : Matrix n n R},
  A.IsIrreducible → Quiver.IsSStronglyConnected n
Defined in
Mathlib.LinearAlgebra.Matrix.Irreducible.Defs
Cited by
3 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
RingLinearOrder
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Around this declaration

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

Matrix.isIrreducible_iff_exists_pow_pos · cited by 1Matrix.isIrreducible_iff_…Matrix.IsIrreducible.transpose · cited by 1IsIrreducible.transposeMatrix.IsIrreducible.exists_pos · cited by 0IsIrreducible.exists_posLinearOrder · cited by 8572LinearOrderRing · cited by 7463RingMatrix · cited by 4303MatrixMatrix.IsIrreducible · cited by 8Matrix.IsIrreducibleQuiver.IsSStronglyConnected · cited by 8Quiver.IsSStronglyConnect…Matrix.toQuiver · cited by 6Matrix.toQuiverIsIrreducible.connectedCITED BYCITES

Cites6

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Cited by3

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