Theorems · Theorem · linear algebra

Matrix.mem_rowStochastic_iff_sum

∀ {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},
  M ∈ Matrix.rowStochastic R n ↔ (∀ (i j : n), 0 ≤ M i j) ∧ ∀ (i : n), ∑ j, M i j = 1

A square matrix is row stochastic if each element is non-negative and row sums to one.

Defined in

Mathlib.LinearAlgebra.Matrix.Stochastic

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqSemiringPartialOrderIsOrderedRing