Theorems · Theorem · linear algebra
Matrix.separatingRight_iff_det_ne_zero
∀ {n : Type u_1} [inst : Fintype n] {A : Type u_4} [inst_1 : CommRing A] [IsDomain A] {M : Matrix n n A}
[inst_3 : DecidableEq n], M.SeparatingRight ↔ M.det ≠ 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsDomainstatement and proof · cited by 2,196
- Matrix.detstatement · cited by 665
- Matrix.SeparatingRightstatement · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.nondegenerate_iff_separatingRightproof · cited by 2
- LinearMap.separatingRight_toLinearMap₂'_iff_det_ne_zeroproof · cited by 1
- LinearMap.separatingRight_iff_det_ne_zeroproof · cited by 1