Theorems · Theorem · linear algebra
Matrix.one_vecMul_of_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 ∈ Matrix.rowStochastic R n → M.mulVec 1 = 1The all-ones column vector multiplied with a row stochastic matrix is 1.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Stochastic
- Cited by
- 0 results in Mathlib
- 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
- Matrix.rowStochasticstatement and proof · cited by 18
- Matrix.mem_rowStochasticproof · cited by 1
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