Theorems · Theorem · linear algebra
extremePoints_doublyStochastic
∀ {R : Type u_1} {n : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : Field R] [inst_3 : LinearOrder R]
[inst_4 : IsStrictOrderedRing R],
Set.extremePoints R ↑(doublyStochastic R n) = {x | ∃ σ, Equiv.Perm.permMatrix R σ = x}The set of extreme points of the doubly stochastic matrices is the set of permutation matrices.
- Defined in
- Mathlib.Analysis.Convex.Birkhoff
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement and proof · cited by 8,199
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Set.ofPredstatement and proof · cited by 6,101
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Equiv.Permstatement and proof · cited by 1,375
- Set.Iooproof · cited by 1,214
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