| Title:
|
$\mathcal {D}_{n,r}$ is not potentially nilpotent for $n \geq 4r-2$ (English) |
| Author:
|
Shao, Yanling |
| Author:
|
Gao, Yubin |
| Author:
|
Gao, Wei |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
671-679 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An $n\times n$ sign pattern $\mathcal {A}$ is said to be potentially nilpotent if there exists a nilpotent real matrix $B$ with the same sign pattern as $\mathcal {A}$. Let $\mathcal {D}_{n,r}$ be an $n\times n$ sign pattern with $2\leq r \leq n$ such that the superdiagonal and the $(n,n)$ entries are positive, the $(i,1)$ $(i=1, \dots , r)$ and $(i,i-r+1)$ $(i=r+1, \dots , n)$ entries are negative, and zeros elsewhere. We prove that for $r\geq 3$ and $n \geq 4r-2$, the sign pattern $\mathcal {D}_{n,r}$ is not potentially nilpotent, and so not spectrally arbitrary. (English) |
| Keyword:
|
sign pattern |
| Keyword:
|
potentially nilpotent pattern |
| Keyword:
|
spectrally arbitrary pattern |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 06644026 |
| idMR:
|
MR3556860 |
| DOI:
|
10.1007/s10587-016-0285-7 |
| . |
| Date available:
|
2016-10-01T15:15:45Z |
| Last updated:
|
2023-10-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145864 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Garnett, C., Shader, B. L.: A proof of the $T_n$ conjecture: Centralizers, Jacobians and spectrally arbitrary sign patterns.Linear Algebra Appl. 436 (2012), 4451-4458. Zbl 1244.15020, MR 2917422 |
| Reference:
|
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| . |
