Theorems · Theorem · linear algebra
Matrix.reindex_mem_rowStochastic_iff
∀ {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 : Type u_3} [inst_5 : Fintype m] [inst_6 : DecidableEq m]
{M : Matrix n n R} {e₁ e₂ : n ≃ m}, (Matrix.reindex e₁ e₂) M ∈ Matrix.rowStochastic R m ↔ M ∈ Matrix.rowStochastic R nReindexing a matrix preserves row-stochasticity.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Stochastic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- Submonoidstatement · cited by 3,086
- IsOrderedRingstatement and proof · cited by 777
- Matrix.submatrixproof · cited by 183
- Matrix.reindexstatement and proof · cited by 102
- Equiv.symm_comp_selfproof · cited by 28
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.reindex_mem_colStochastic_iffproof · cited by 1