Theorems · Theorem · group theory
Matrix.GeneralLinearGroup.det_scalar
∀ {n : Type u} [inst : DecidableEq n] [inst_1 : Fintype n] {R : Type v} [inst_2 : CommRing R] (u : Rˣ),
Matrix.GeneralLinearGroup.det ((Matrix.GeneralLinearGroup.scalar n) u) = u ^ Fintype.card n- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- Fintype.cardstatement and proof · cited by 1,386
- Matrix.GeneralLinearGroupstatement · cited by 556
- Finset.prod_constproof · cited by 154
- Units.extproof · cited by 86
- Matrix.GeneralLinearGroup.detstatement · cited by 58
Cited by3
Results whose statement or proof uses this declaration.
- UpperHalfPlane.glScalar_smulproof · cited by 2
- Matrix.SpecialLinearGroup.toGL_mem_center_iffproof · cited by 0
- Matrix.ProjectiveSpecialLinearGroup.toPGL_surj_iffproof · cited by 0