Theorems · Theorem · linear algebra

Matrix.transpose_mem_colStochastic_iff_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},
  M.transpose ∈ Matrix.colStochastic R n ↔ M ∈ Matrix.rowStochastic R n

The transpose of a matrix is column stochastic matrix if it is row stochastic.

Defined in

Mathlib.LinearAlgebra.Matrix.Stochastic

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqSemiringPartialOrderIsOrderedRing