Theorems · Theorem · linear algebra
Matrix.nonsing_inv_mul_cancel_right
∀ {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 m n α), IsUnit A.det → B * A⁻¹ * A = B- Cited by
- 2 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.
Cites8
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.nonsing_inv_mulproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- SymplecticGroup.transpose_memproof · cited by 2
- Matrix.inv_mul_cancel_right_of_invertibleproof · cited by 1