Theorems · Theorem · linear algebra
Matrix.cRank_le_card_width
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Semiring R] [StrongRankCondition R] [inst_2 : Fintype n]
(A : Matrix m n R), A.cRank ≤ ↑(Fintype.card n)- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- Fintype.cardstatement and proof · cited by 1,386
- Cardinal.mkproof · cited by 942
- Cardinal.liftproof · cited by 583
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.eRank_le_card_widthproof · cited by 0