| Title:
|
A new family of spectrally arbitrary ray patterns (English) |
| Author:
|
Mei, Yinzhen |
| Author:
|
Gao, Yubin |
| Author:
|
Shao, Yanling |
| Author:
|
Wang, Peng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
1049-1058 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An $n\times n$ ray pattern $\mathcal {A}$ is called a spectrally arbitrary ray pattern if the complex matrices in $Q(\mathcal {A})$ give rise to all possible complex polynomials of degree $n$. \endgraf In a paper of Mei, Gao, Shao, and Wang (2014) was proved that the minimum number of nonzeros in an $n\times n$ irreducible spectrally arbitrary ray pattern is $3n-1$. In this paper, we introduce a new family of spectrally arbitrary ray patterns of order $n$ with exactly $3n-1$ nonzeros. (English) |
| Keyword:
|
ray pattern |
| Keyword:
|
potentially nilpotent |
| Keyword:
|
spectrally arbitrary ray pattern |
| MSC:
|
15A18 |
| MSC:
|
15A29 |
| idZBL:
|
Zbl 06674861 |
| idMR:
|
MR3572922 |
| DOI:
|
10.1007/s10587-016-0309-3 |
| . |
| Date available:
|
2016-11-26T20:49:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145917 |
| . |
| Reference:
|
[1] Drew, J. H., Johnson, C. R., Olesky, D. D., Driessche, P. van den: Spectrally arbitrary patterns.Linear Algebra Appl. 308 (2000), 121-137. MR 1751135 |
| Reference:
|
[2] Gao, Y., Shao, Y.: New classes of spectrally arbitrary ray patterns.Linear Algebra Appl. 434 (2011), 2140-2148. Zbl 1272.15019, MR 2781682 |
| Reference:
|
[3] McDonald, J. J., Stuart, J.: Spectrally arbitrary ray patterns.Linear Algebra Appl. 429 (2008), 727-734. Zbl 1143.15007, MR 2428126 |
| Reference:
|
[4] Mei, Y., Gao, Y., Shao, Y., Wang, P.: The minimum number of nonzeros in a spectrally arbitrary ray pattern.Linear Algebra Appl. 453 (2014), 99-109. Zbl 1328.15020, MR 3201687 |
| . |
