Theorems · Theorem · linear algebra
Matrix.nonsing_inv_apply_not_isUnit
∀ {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⁻¹ = 0- Cited by
- 7 results in Mathlib
- Foundations
- Depth 97 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.
Cites9
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
- zero_smulproof · cited by 716
- Matrix.detstatement and proof · cited by 665
- Matrix.adjugateproof · cited by 64
- Ring.inverse_non_unitproof · cited by 26
- Matrix.inv_defproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.nonsing_inv_eq_ringInverseproof · cited by 7
- Matrix.det_nonsing_invproof · cited by 4
- Matrix.nonsing_inv_cancel_or_zeroproof · cited by 4
- Matrix.PosSemidef.invproof · cited by 2
- Matrix.inv_zeroproof · cited by 2
- Matrix.inv_inv_invproof · cited by 0
- Matrix.inv_kroneckerproof · cited by 0