Theorems · Theorem · linear algebra
Matrix.det_nonsing_inv
∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] (A : Matrix n n α),
A⁻¹.det = Ring.inverse A.det- Cited by
- 4 results in Mathlib
- Foundations
- Depth 103 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.
Cites20
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
- IsUnitproof · cited by 1,602
- IsEmptyproof · cited by 759
- Matrix.detstatement and proof · cited by 665
- Invertibleproof · cited by 549
- isEmpty_or_nonemptyproof · cited by 269
- Invertible.invOfproof · cited by 268
- Ring.inversestatement and proof · cited by 160
- Ring.inverse_non_unitproof · cited by 26
- IsUnit.nonempty_invertibleproof · cited by 16
Cited by4
Results whose statement or proof uses this declaration.
- IsUnit.det_zpowproof · cited by 2
- Matrix.isUnit_nonsing_inv_det_iffproof · cited by 2
- Matrix.GeneralLinearGroup.det_surjectiveproof · cited by 1
- Matrix.charpoly_invproof · cited by 0