Theorems · Theorem · linear algebra
Matrix.mul_nonsing_inv
∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] (A : Matrix n n α),
IsUnit A.det → A * A⁻¹ = 1The nonsing_inv of A is a right inverse.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 104 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.
Cites10
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
- Invertibleproof · cited by 549
- mul_invOf_selfproof · cited by 28
- IsUnit.nonempty_invertibleproof · cited by 16
- Matrix.isUnit_iff_isUnit_detproof · cited by 12
- Matrix.invOf_eq_nonsing_invproof · cited by 11
Cited by12
Results whose statement or proof uses this declaration.
- Matrix.nonsing_inv_cancel_or_zeroproof · cited by 4
- Matrix.mul_nonsing_inv_cancel_leftproof · cited by 4
- Matrix.nonsing_inv_nonsing_invproof · cited by 3
- Matrix.mul_nonsing_inv_cancel_rightproof · cited by 2
- AffineBasis.toMatrix_inv_vecMul_toMatrixproof · cited by 1
- Matrix.mul_inv_of_invertibleproof · cited by 1
- Matrix.zpow_sub_oneproof · cited by 1
- Matrix.pow_sub'proof · cited by 0
- Matrix.inv_injproof · cited by 0
- Matrix.inv_kroneckerproof · cited by 0
- Matrix.invertibleOfIsUnitDetproof · cited by 0
- Matrix.GeneralLinearGroup.coe_map_mul_map_invproof · cited by 0