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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F22%3A00553621" target="_blank" >RIV/61389005:_____/22:00553621 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/5.0079385" target="_blank" >https://doi.org/10.1063/5.0079385</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0079385" target="_blank" >10.1063/5.0079385</a>

Result language
angličtina
Original language name
Which metrics are consistent with a given pseudo-hermitian matrix?
Original language description
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).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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