Theorems · Theorem · linear algebra

Matrix.sum_col_of_mem_colStochastic

∀ {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.colStochastic R n → ∀ (i : n), ∑ j, M j i = 1

Each column sum of a column stochastic matrix is 1.

Defined in

Mathlib.LinearAlgebra.Matrix.Stochastic

Cited by

2 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqSemiringPartialOrderIsOrderedRing