Theorems · Theorem · linear algebra
Matrix.inv_submatrix_equiv
∀ {m : Type u} {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α]
[inst_3 : Fintype m] [inst_4 : DecidableEq m] (A : Matrix m m α) (e₁ e₂ : n ≃ m),
(A.submatrix ⇑e₁ ⇑e₂)⁻¹ = A⁻¹.submatrix ⇑e₂ ⇑e₁- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Equivstatement and proof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsUnitproof · cited by 1,602
- Invertibleproof · cited by 549
- Iff.notproof · cited by 489
- Invertible.invOfproof · cited by 268
- Matrix.submatrixstatement and proof · cited by 183
- Ring.inverseproof · cited by 160
- Ring.inverse_non_unitproof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.inv_reindexproof · cited by 0