Theorems · Theorem · linear algebra
Matrix.mul_nonsing_inv_cancel_left
∀ {m : Type u} {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α]
(A : Matrix n n α) (B : Matrix n m α), IsUnit A.det → A * (A⁻¹ * B) = B- Cited by
- 4 results in Mathlib
- Foundations
- Depth 105 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.
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 and proof · cited by 1,602
- Matrix.detstatement and proof · cited by 665
- Matrix.one_mulproof · cited by 30
- Matrix.mul_nonsing_invproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.mul_inv_cancel_left_of_invertibleproof · cited by 3
- SymplecticGroup.transpose_memproof · cited by 2
- Matrix.det_add_mulproof · cited by 0
- Matrix.det_add_replicateCol_mul_replicateRowproof · cited by 0