| Title:
|
Computing the determinantal representations of hyperbolic forms (English) |
| Author:
|
Chien, Mao-Ting |
| Author:
|
Nakazato, Hiroshi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
633-651 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The numerical range of an $n\times n$ matrix is determined by an $n$ degree hyperbolic ternary form. Helton-Vinnikov confirmed conversely that an $n$ degree hyperbolic ternary form admits a symmetric determinantal representation. We determine the types of Riemann theta functions appearing in the Helton-Vinnikov formula for the real symmetric determinantal representation of hyperbolic forms for the genus $g=1$. We reformulate the Fiedler-Helton-Vinnikov formulae for the genus $g=0,1$, and present an elementary computation of the reformulation. Several examples are provided for computing the real symmetric matrices using the reformulation. (English) |
| Keyword:
|
determinantal representation |
| Keyword:
|
hyperbolic form |
| Keyword:
|
Riemann theta function |
| Keyword:
|
numerical range |
| MSC:
|
14Q05 |
| MSC:
|
15A60 |
| idZBL:
|
Zbl 06644024 |
| idMR:
|
MR3556858 |
| DOI:
|
10.1007/s10587-016-0283-9 |
| . |
| Date available:
|
2016-10-01T15:13:54Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145862 |
| . |
| Reference:
|
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| Reference:
|
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