Theorems · Theorem · linear algebra
LinearIndependent.rank_matrix
∀ {m : Type um} {n : Type un} {R : Type uR} [inst : Fintype n] [inst_1 : Field R] [inst_2 : Fintype m]
{M : Matrix m n R}, LinearIndependent R M.row → M.rank = Fintype.card m- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Set.rangeproof · cited by 4,705
- Matrixstatement and proof · cited by 4,303
- Module.finrankproof · cited by 1,770
- Submodule.spanproof · cited by 1,504
- Fintype.cardstatement and proof · cited by 1,386
- LinearIndependentstatement and proof · cited by 560
- Matrix.rankstatement · cited by 48
- Matrix.rowstatement and proof · cited by 40
- linearIndependent_iff_card_eq_finrank_spanproof · cited by 5
- Matrix.rank_eq_finrank_span_rowproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Configuration.ofField.crossProduct_eq_zero_of_dotProduct_eq_zeroproof · cited by 1