Theorems · Definition · linear algebra
Set.finrank
(R : Type u) → {M : Type v} → [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [Module R M] → Set M → ℕThe rank of a set of vectors as a natural number.
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Module.finrankproof · cited by 1,770
- Submodule.spanproof · cited by 1,504
Cited by9
Results whose statement or proof uses this declaration.
- linearIndependent_iff_card_eq_finrank_spanstatement and proof · cited by 5
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- Real.finrank_eq_int_finrank_of_discretestatement and proof · cited by 1
- finrank_range_le_cardstatement · cited by 1
- affineIndependent_iff_finrank_vectorSpan_eqproof · cited by 1
- finrank_span_finset_le_cardstatement · cited by 1
- linearIndependent_iff_card_le_finrank_spanstatement and proof · cited by 0
- Set.finrank_emptystatement · cited by 0
- Set.finrank_monostatement · cited by 0