Theorems · Theorem · linear algebra
doublyStochastic_eq_rowStochastic_inf_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],
doublyStochastic R n = Matrix.rowStochastic R n ⊓ Matrix.colStochastic R nA matrix is doubly stochastic if and only if it is both row and column stochastic.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- IsOrderedRingstatement and proof · cited by 777
- Matrix.mulVecproof · cited by 267
- Matrix.vecMulproof · cited by 148
- Submonoid.extproof · cited by 48
- doublyStochasticstatement · cited by 22
- Matrix.colStochasticstatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- mem_doublyStochastic_iff_mem_rowStochastic_and_mem_colStochasticproof · cited by 0