Theorems · Theorem · number theory
UpperHalfPlane.exists_gl_smul_eq_self_iff_trace_eq_zero
∀ {g : GL (Fin 2) ℝ}, (↑g).det < 0 → ((∃ z, g • z = z) ↔ (↑g).trace = 0)An orientation-reversing isometry of the hyperbolic plane has a fixed point iff the corresponding matrix has zero trace.
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- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
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- Complex.ofRealproof · cited by 1,654
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