Theorems · Theorem · linear algebra
mulVec_one_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 → M.mulVec 1 = 1A doubly stochastic matrix multiplied with the all-ones column vector is 1.
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- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- IsOrderedRingstatement and proof · cited by 777
- Matrix.mulVecstatement · cited by 267
- doublyStochasticstatement and proof · cited by 22
- mem_doublyStochasticproof · cited by 2
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