Which metrics are consistent with a given pseudo-hermitian matrix?

Joshua Feinberg, Miloslav Znojil

Research output: Contribution to journalArticlepeer-review


Given a diagonalizable N × N matrix H, whose non-degenerate spectrum consists of p pairs of complex conjugate eigenvalues and additional N-2p real eigenvalues, we determine all metrics M, of all possible signatures, with respect to which H is pseudo-hermitian. In particular, we show that any compatible M must have p pairs of opposite eigenvalues in its spectrum so that p is the minimal number of both positive and negative eigenvalues of M. We provide explicit parameterization of the space of all admissible metrics and show that it is topologically a p-dimensional torus tensored with an appropriate power of the group Z2.

Original languageEnglish
Article number013505
JournalJournal of Mathematical Physics
Issue number1
StatePublished - 1 Jan 2022

Bibliographical note

Publisher Copyright:
© 2022 Author(s).

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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