Theorems · Theorem · linear algebra
Matrix.eRank_le_card_width
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Semiring R] [StrongRankCondition R] (A : Matrix m n R),
A.eRank ≤ ENat.card n- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringStrongRankCondition
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
- Fintypeproof · cited by 7,736
- ENatstatement and proof · cited by 4,985
- Matrixstatement and proof · cited by 4,303
- Finiteproof · cited by 3,029
- Fintype.cardproof · cited by 1,386
- StrongRankConditionstatement and proof · cited by 286
- Fintype.ofFiniteproof · cited by 255
- ENat.cardstatement · cited by 89
- ENat.card_eq_coe_fintype_cardproof · cited by 15
- Matrix.eRankstatement and proof · cited by 11
- Cardinal.toENat_le_natCastproof · cited by 6
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