Theorems · Theorem · linear algebra
Matrix.det_isEmpty
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] [IsEmpty n]
{A : Matrix n n R}, A.det = 1- Cited by
- 9 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Unitsproof · cited by 2,804
- Finset.sum_congrproof · cited by 2,323
- Equiv.Permproof · cited by 1,375
- one_smulproof · cited by 1,374
- IsEmptystatement and proof · cited by 759
- Matrix.detstatement · cited by 665
- Finset.prod_congrproof · cited by 646
- Finset.sum_singletonproof · cited by 251
Cited by9
Results whose statement or proof uses this declaration.
- Matrix.det_fin_zeroproof · cited by 5
- Matrix.coe_det_isEmptyproof · cited by 5
- Matrix.det_nonsing_invproof · cited by 4
- Module.Basis.det_isEmptyproof · cited by 4
- LinearMap.det_eq_one_of_finrank_eq_zeroproof · cited by 3
- LinearMap.det_eq_one_of_subsingletonproof · cited by 3
- Matrix.det_eq_one_of_card_eq_zeroproof · cited by 2
- Matrix.BlockTriangular.det_fintypeproof · cited by 2
- Matrix.det_detproof · cited by 1