Theorems · Definition · group theory
Matrix.symplecticGroup
(l : Type u_1) →
(R : Type u_2) →
[inst : DecidableEq l] → [inst_1 : CommRing R] → [inst_2 : Fintype l] → Submonoid (Matrix (l ⊕ l) (l ⊕ l) R)The group of symplectic matrices over a ring R.
- Defined in
- Mathlib.LinearAlgebra.SymplecticGroup
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqCommRingFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.ofPredproof · cited by 6,101
- Matrixstatement and proof · cited by 4,303
- Submonoidstatement · cited by 3,086
- Matrix.transposeproof · cited by 389
- Matrix.Jproof · cited by 20
Cited by16
Results whose statement or proof uses this declaration.
- SymplecticGroup.mem_iffstatement · cited by 6
- SymplecticGroup.inv_left_mul_auxstatement and proof · cited by 2
- SymplecticGroup.mem_iff'statement · cited by 2
- SymplecticGroup.transpose_memstatement and proof · cited by 2
- SymplecticGroup.coe_invstatement and proof · cited by 1
- SymplecticGroup.map_memstatement and proof · cited by 1
- SymplecticGroup.symJstatement · cited by 1
- SymplecticGroup.symplectic_detstatement and proof · cited by 1
- SymplecticGroup.transpose_mem_iffstatement and proof · cited by 1
- SymplecticGroup.J_memstatement · cited by 0
- SymplecticGroup.coe_Jstatement · cited by 0
- SymplecticGroup.coe_inv'statement and proof · cited by 0