Theorems · Theorem · linear algebra
Matrix.det_diagonal
∀ {n : Type u_2} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] {d : n → R},
(Matrix.diagonal d).det = ∏ i, d i- Cited by
- 27 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqFintypeCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Finset.univstatement and proof · cited by 3,473
- one_mulproof · cited by 2,841
- Finset.prodstatement and proof · cited by 2,356
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valproof · cited by 1,966
- Equiv.Permproof · cited by 1,375
- Matrix.detstatement · cited by 665
- Int.cast_oneproof · cited by 371
- Finset.mem_univproof · cited by 361
Cited by27
Results whose statement or proof uses this declaration.
- Matrix.det_oneproof · cited by 35
- Polynomial.resultant_zero_left_degproof · cited by 13
- Matrix.det_smulproof · cited by 11
- Matrix.charpoly_diagonalproof · cited by 4
- Algebra.norm_algebraMap_of_basisproof · cited by 3
- Matrix.SpecialLinearGroup.diagonal_neZeroproof · cited by 3
- Matrix.GeneralLinearGroup.det_scalarproof · cited by 3
- Matrix.SpecialLinearGroup.mem_center_iffproof · cited by 2
- Module.Basis.det_unitsSMul_selfproof · cited by 2
- Submodule.natAbs_det_equivproof · cited by 2
- Matrix.charpoly_mul_comm'proof · cited by 2
- Real.smul_map_diagonal_volume_piproof · cited by 1