Theorems · Theorem · linear algebra
Matrix.isUnit_det_of_left_inverse
∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] {A B : Matrix n n α},
B * A = 1 → IsUnit A.det- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 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.
Cites6
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
- isUnit_of_invertibleproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.Commute.zpow_rightproof · cited by 3
- LinearEquiv.isUnit_detproof · cited by 2
- Matrix.zpow_add_of_nonposproof · cited by 0
- Matrix.zpow_add_one_of_ne_neg_oneproof · cited by 0
- Matrix.det_ne_zero_of_left_inverseproof · cited by 0