Theorems · Theorem · linear algebra
Matrix.nonneg_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 → ∀ {i j : n}, 0 ≤ M i jEvery entry of a row stochastic matrix is nonnegative.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Stochastic
- Cited by
- 3 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.
Cites7
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
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- IsOrderedRingstatement and proof · cited by 777
- Matrix.rowStochasticstatement and proof · cited by 18
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.reindex_mem_rowStochasticproof · cited by 1
- Matrix.nonneg_mulVec_of_mem_rowStochasticproof · cited by 0
- Matrix.nonneg_vecMul_of_mem_rowStochasticproof · cited by 0