Theorems · Theorem · group theory
Matrix.J_squared
∀ (l : Type u_1) (R : Type u_2) [inst : DecidableEq l] [inst_1 : CommRing R] [inst_2 : Fintype l], Matrix.J l R * Matrix.J l R = -1
- Defined in
- Mathlib.LinearAlgebra.SymplecticGroup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 73 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.
Cites14
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
- Matrixstatement and proof · cited by 4,303
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- neg_zeroproof · cited by 542
- Matrix.fromBlocksproof · cited by 108
- Matrix.one_mulproof · cited by 30
- Matrix.Jstatement · cited by 20
- Matrix.zero_mulproof · cited by 16
- Matrix.fromBlocks_multiplyproof · cited by 12
- Matrix.neg_mulproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- SymplecticGroup.inv_left_mul_auxproof · cited by 2
- Matrix.J_det_mul_J_detproof · cited by 1
- Matrix.J_invproof · cited by 1