Theorems · Theorem · linear algebra

sum_col_of_mem_doublyStochastic

∀ {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 ∈ doublyStochastic R n → ∀ (j : n), ∑ i, M i j = 1

Each column sum of a doubly stochastic matrix is 1.

Defined in

Mathlib.Analysis.Convex.DoublyStochasticMatrix

Cited by

0 results in Mathlib

Foundations

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

Assumes

FintypeDecidableEqSemiringPartialOrderIsOrderedRing