Theorems · Theorem · linear algebra
Matrix.inv_eq_left_inv
∀ {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 → A⁻¹ = BIf matrix A is left invertible, then its inverse equals its left inverse.
- Cited by
- 9 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.
Cites5
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
- Matrix.invOf_eq_nonsing_invproof · cited by 11
- invOf_eq_left_invproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Matrix.inv_eq_right_invproof · cited by 4
- Matrix.BlockTriangular.inv_toBlockproof · cited by 1
- Matrix.left_inv_eq_left_invproof · cited by 1
- Matrix.right_inv_eq_left_invproof · cited by 0
- Matrix.inv_smulproof · cited by 0
- Matrix.inv_smul'proof · cited by 0
- Matrix.inv_adjugateproof · cited by 0
- SymplecticGroup.coe_inv'proof · cited by 0
- SymplecticGroup.inv_eq_symplectic_invproof · cited by 0