Theorems · Theorem · group theory
Matrix.SpecialLinearGroup.diagonal_neZero
∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : Fintype ι] [inst_2 : DecidableEq ι] (D : ι → F),
(Matrix.diagonal D).det = 1 → ∀ (j : ι), D j ≠ 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- MulZeroClass.zero_mulproof · cited by 1,625
- Finset.filterproof · cited by 949
- Matrix.detstatement and proof · cited by 665
- Matrix.diagonalstatement and proof · cited by 314
- Finset.prod_insertproof · cited by 109
- zero_ne_oneproof · cited by 90
- Matrix.det_diagonalproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.SpecialLinearGroup.diag_commutestatement and proof · cited by 2
- Matrix.SpecialLinearGroup.diag_eq_diag2n_prodstatement and proof · cited by 1
- Matrix.SpecialLinearGroup.diagonal_transvection_induction'proof · cited by 1