Theorems · Theorem · linear algebra

reindex_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 : Type u_3} [inst_5 : Fintype m] [inst_6 : DecidableEq m]
  {M : Matrix n n R} {e₁ e₂ : n ≃ m}, M ∈ doublyStochastic R n → (Matrix.reindex e₁ e₂) M ∈ doublyStochastic R m

Reindexing a matrix preserves double stochasticity.

Defined in

Mathlib.Analysis.Convex.DoublyStochasticMatrix

Cited by

0 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeDecidableEqSemiringPartialOrderIsOrderedRingFintypeDecidableEq