Theorems · Theorem · linear algebra
Matrix.cRank_le_card_height
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Semiring R] [StrongRankCondition R] [inst_2 : Fintype m]
(A : Matrix m n R), A.cRank ≤ ↑(Fintype.card m)- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 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.
Cites14
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
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- le_reflproof · cited by 2,061
- Submodule.spanproof · cited by 1,504
- Fintype.cardstatement and proof · cited by 1,386
- Matrix.transposeproof · cited by 389
- StrongRankConditionstatement and proof · cited by 286
- Matrix.cRankstatement · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.eRank_le_card_heightproof · cited by 0