Theorems · Theorem · linear algebra
Matrix.rank_submatrix
∀ {m : Type um} {m₀ : Type um₀} {n : Type un} {n₀ : Type un₀} {R : Type uR} [inst : Fintype n] [inst_1 : Fintype n₀]
[inst_2 : CommSemiring R] (A : Matrix m n R) (em : m₀ ≃ m) (en : n₀ ≃ n), (A.submatrix ⇑em ⇑en).rank = A.rank- Defined in
- Mathlib.LinearAlgebra.Matrix.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeFintypeCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Equiv.symmproof · cited by 3,681
- Matrix.submatrixstatement · cited by 183
- Matrix.rankstatement · cited by 48
- Matrix.rank_reindexproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Echelon.Decomposition.rank_eqproof · cited by 0