Theorems · Theorem · linear algebra
Matrix.isUnit_det_of_invertible
∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] (A : Matrix n n α)
[Invertible A], IsUnit A.det- Cited by
- 6 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 1,602
- Matrix.detstatement and proof · cited by 665
- Invertiblestatement and proof · cited by 549
- isUnit_of_invertibleproof · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.inv_mul_of_invertibleproof · cited by 7
- Matrix.mul_inv_cancel_left_of_invertibleproof · cited by 3
- Matrix.mul_inv_cancel_right_of_invertibleproof · cited by 3
- Matrix.inv_mul_cancel_left_of_invertibleproof · cited by 2
- Matrix.mul_inv_of_invertibleproof · cited by 1
- Matrix.inv_mul_cancel_right_of_invertibleproof · cited by 1