Theorems · Theorem · linear algebra
Matrix.nonsingular_submatrix_equiv_iff
∀ {n : Type u_1} {m : Type u_2} {R : Type u_3} [inst : Fintype m] [inst_1 : Fintype n] [inst_2 : DecidableEq m]
[inst_3 : DecidableEq n] [inst_4 : CommSemiring R] {A : Matrix n n R} {e₁ e₂ : m ≃ n},
(A.submatrix ⇑e₁ ⇑e₂).Nonsingular ↔ A.Nonsingular- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Matrix.submatrixstatement · cited by 183
- Matrix.Nonsingularstatement · cited by 27
- Matrix.IsDetpBalancedproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.Nonsingular.submatrix_equivproof · cited by 0