Theorems · Theorem · linear algebra
Matrix.submatrix_submatrix
∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {o : Type u_4} {α : Type v} {l₂ : Type u_10} {o₂ : Type u_11}
(A : Matrix m n α) (r₁ : l → m) (c₁ : o → n) (r₂ : l₂ → l) (c₂ : o₂ → o),
(A.submatrix r₁ c₁).submatrix r₂ c₂ = A.submatrix (r₁ ∘ r₂) (c₁ ∘ c₂)- Defined in
- Mathlib.LinearAlgebra.Matrix.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Matrix.extproof · cited by 540
- Matrix.submatrixstatement · cited by 183
Cited by24
Results whose statement or proof uses this declaration.
- Matrix.det_succ_rowproof · cited by 6
- Matrix.lift_cRank_submatrixproof · cited by 3
- Matrix.Nonsingular.of_linearIndependent_colproof · cited by 3
- Matrix.det_fin_threeproof · cited by 3
- Matrix.IsTotallyUnimodular.submatrixproof · cited by 2
- NumberField.Units.finrank_mul_regOfFamily_eq_detproof · cited by 2
- Matrix.isHermitian_submatrix_equivproof · cited by 1
- Matrix.rank_submatrix_leproof · cited by 1
- Matrix.posSemidef_submatrix_equivproof · cited by 1
- Matrix.isDetpBalanced_submatrix_equiv_iffproof · cited by 1
- Matrix.IsTotallyUnimodular.fromRows_unitlikeproof · cited by 1