Theorems · Theorem · linear algebra
Matrix.nonsing_inv_nonsing_inv
∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] (A : Matrix n n α),
IsUnit A.det → A⁻¹⁻¹ = A- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsUnitstatement and proof · cited by 1,602
- Matrix.detstatement and proof · cited by 665
- Matrix.mul_assocproof · cited by 56
- Matrix.mul_oneproof · cited by 45
- Matrix.one_mulproof · cited by 30
- Matrix.mul_nonsing_invproof · cited by 11
- Matrix.isUnit_nonsing_inv_detproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.zpow_negproof · cited by 5
- Matrix.zpow_mulproof · cited by 1
- Matrix.inv_inv_invproof · cited by 0