Theorems · Theorem · linear algebra
Matrix.cRank_toNat_eq_rank
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : CommSemiring R] (A : Matrix m n R),
Cardinal.toNat A.cRank = A.rank- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeCommSemiring
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Cardinalstatement · cited by 2,598
- MonoidWithZeroHomstatement · cited by 704
- Cardinal.toNatstatement · cited by 153
- Matrix.rankstatement and proof · cited by 48
- Matrix.cRankstatement · cited by 16
- Matrix.rank_eq_finrank_span_colsproof · cited by 3
- Matrix.cRank_toNat_eq_finrankproof · cited by 1
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