Theorems · Theorem · number theory
UpperHalfPlane.gl_smul_eq_self_iff_eq_fixedPt
∀ {g : GL (Fin 2) ℝ} {z : UpperHalfPlane},
0 < (↑g).det → ∀ (hell : g.IsElliptic), g • z = z ↔ z = UpperHalfPlane.fixedPt g hellThe action of an elliptic orientation preserving matrix on ℍ
has a unique fixed point given by fixedPt.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites69
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complexproof · cited by 5,565
- Matrixstatement · cited by 4,303
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- LT.lt.leproof · cited by 2,189
- MulZeroClass.mul_zeroproof · cited by 2,091
- Units.valstatement and proof · cited by 1,966
- Nat.cast_zeroproof · cited by 1,870
- absproof · cited by 1,814
Cited by1
Results whose statement or proof uses this declaration.
- UpperHalfPlane.forall_smul_eq_self_iff_mem_centerproof · cited by 0