Unified approach to reciprocal matrices with Kippenhahn curves containing elliptical components
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909235156090880 |
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| author | Jiang, Muyan Spitkovsky, Ilya M. |
| author_facet | Jiang, Muyan Spitkovsky, Ilya M. |
| contents | Reciprocal matrices are tridiagonal matrices $(a_{ij})_{i,j=1}^n$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,\ldots,n-1$. For these matrices, criteria are established under which their Kippenhahn curves contain elliptical components or even consist completely of such. These criteria are in terms of system of homogeneous polynomial equations in variables $(\left|a_{j,j+1}\right|-\left|a_{j+1,j}\right|)^2$, and established via a unified approach across arbitrary dimensions. The results are illustrated, and specific numerical examples provided, for $n=7$ thus generalizing earlier work in the lower dimensional setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unified approach to reciprocal matrices with Kippenhahn curves containing elliptical components Jiang, Muyan Spitkovsky, Ilya M. Functional Analysis 47B36, 15A60 Reciprocal matrices are tridiagonal matrices $(a_{ij})_{i,j=1}^n$ with constant main diagonal and such that $a_{i,i+1}a_{i+1,i}=1$ for $i=1,\ldots,n-1$. For these matrices, criteria are established under which their Kippenhahn curves contain elliptical components or even consist completely of such. These criteria are in terms of system of homogeneous polynomial equations in variables $(\left|a_{j,j+1}\right|-\left|a_{j+1,j}\right|)^2$, and established via a unified approach across arbitrary dimensions. The results are illustrated, and specific numerical examples provided, for $n=7$ thus generalizing earlier work in the lower dimensional setting. |
| title | Unified approach to reciprocal matrices with Kippenhahn curves containing elliptical components |
| topic | Functional Analysis 47B36, 15A60 |
| url | https://arxiv.org/abs/2407.00804 |