Sánchez Soto, Luis LorenzoMonzón Serrano, Juan José2023-06-172023-06-172018-102073-899410.3390/sym10100494https://hdl.handle.net/20.500.14352/12995© 2018 by the authors. Licensee MDPI, Basel, Switzerland Author Contributions: Both authors contributed equally to all aspects of preparing this manuscript. Funding: Financial support from the Spanish MINECO (Grant No. FIS2015-67963-P) is gratefully acknowledged. Acknowledgments: We acknowledge illuminating discussions with José María Montesinos. Conflicts of Interest: The authors declare no conflicts of interest.We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Mobius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttp://dx.doi.org/10.3390/sym10100494https://www.mdpi.comopen access535Non-hermitian hamiltoniansComplex periodic potentialsQuantum-mechanicsPt-symmetryEigenvaluesEquivalentScatteringSpectraÓptica (Física)2209.19 Óptica Física