Theorems · Theorem · linear algebra

Matrix.IsIrreducible.exists_pos

∀ {n : Type u_1} {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] {A : Matrix n n R} [Nontrivial n],
  A.IsIrreducible → ∀ (i : n), ∃ j, 0 < A i j

If A is irreducible and n is non-trivial then every row has a positive entry.

Defined in

Mathlib.LinearAlgebra.Matrix.Irreducible.Defs

Cited by

0 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderNontrivial