Theorems · Theorem · linear algebra
Matrix.rank_le_card_width
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : CommSemiring R] [StrongRankCondition R]
(A : Matrix m n R), A.rank ≤ Fintype.card n- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Fintype.cardstatement · cited by 1,386
- LE.le.trans_eqproof · cited by 328
- StrongRankConditionstatement and proof · cited by 286
- Matrix.rankstatement · cited by 48
- Matrix.mulVecLinproof · cited by 38
- Module.finrank_piproof · cited by 5
- LinearMap.finrank_range_leproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.rank_unitproof · cited by 1
- Matrix.rank_vecMulVec_leproof · cited by 0
- Matrix.rank_le_widthproof · cited by 0