Theorems · Theorem · number theory
UpperHalfPlane.gl_smul_eq_self_iff_re_eq
∀ {g : GL (Fin 2) ℝ} {z : UpperHalfPlane}, (↑g).trace = 0 → ↑g 1 0 = 0 → (g • z = z ↔ z.re = ↑g 0 1 / (2 * ↑g 1 1))If g is an upper triangular matrix with trace zero,
then g fixes the vertical line re z = b / (2 * d).
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- Matrixstatement · cited by 4,303
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valstatement and proof · cited by 1,966
- Complex.ofRealproof · cited by 1,654
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_selfproof · cited by 996
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.forall_smul_eq_self_iff_mem_centerproof · cited by 0