Theorems · Theorem · linear algebra

Matrix.nonneg_mulVec_of_mem_rowStochastic

∀ {R : Type u_1} {n : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : Semiring R]
  [inst_3 : PartialOrder R] [inst_4 : IsOrderedRing R] {M : Matrix n n R} {x : n → R},
  M ∈ Matrix.rowStochastic R n → (∀ (i : n), 0 ≤ x i) → ∀ (j : n), 0 ≤ M.mulVec x j

Right multiplication of a row stochastic matrix by a non-negative vector gives a non-negative vector

Defined in

Mathlib.LinearAlgebra.Matrix.Stochastic

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqSemiringPartialOrderIsOrderedRing