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Which metrics are consistent with a given pseudo-hermitian matrix?
- 1.0553621 - ÚJF 2023 RIV US eng J - Journal Article
Feinberg, J. - Znojil, Miloslav
Which metrics are consistent with a given pseudo-hermitian matrix?
Journal of Mathematical Physics. Roč. 63, č. 1 (2022), č. článku 013505. ISSN 0022-2488. E-ISSN 1089-7658
Institutional support: RVO:61389005
Keywords : pseduo-hermitian * matrix * eigenvalues
OECD category: Pure mathematics
Impact factor: 1.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1063/5.0079385
Given a diagonalizable N x 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 Z(2).
Permanent Link: http://hdl.handle.net/11104/0328375
Number of the records: 1