| Title:
|
On potentially nilpotent double star sign patterns (English) |
| Author:
|
Li, Honghai |
| Author:
|
Li, Jiongsheng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
489-501 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A matrix $\Cal A$ whose entries come from the set $\{+,-,0\}$ is called a {\it sign pattern matrix}, or {\it sign pattern}. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by ${\cal DSSP}(m,2)$, is introduced. We determine all potentially nilpotent sign patterns in ${\cal DSSP}(3,2)$ and ${\cal DSSP}(5,2)$, and prove that one sign pattern in ${\cal DSSP}(3,2)$ is potentially stable. (English) |
| Keyword:
|
sign pattern |
| Keyword:
|
double star |
| Keyword:
|
potentially nilpotent |
| Keyword:
|
potentially stable |
| MSC:
|
05C50 |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 1224.05303 |
| idMR:
|
MR2532386 |
| . |
| Date available:
|
2010-07-20T15:20:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140493 |
| . |
| Reference:
|
[1] Bone, T.: Positive feedback may sometimes promote stability.Linear Algebra Appl. 51 (1983),143-151. Zbl 0515.93042, MR 0699729 |
| Reference:
|
[2] Drew, J. H., Johnson, C. R., Olesky, D. D.: P. van den Driessche, Spectrally arbitrary patterns.Linear Algebra Appl. 308 (2000), 121-137. MR 1751135 |
| Reference:
|
[3] Eschenbach, C. A., Li, Z.: Potentially nilpotent sign pattern matrices.Linear Algebra Appl. 299 (1999), 81-99. Zbl 0941.15012, MR 1723710 |
| Reference:
|
[4] Johnson, C. R., Summers, T. S.: The potentially stable tree sign patterns for dimensions less than five.Linear Algebra Appl. 126 (1989), 1-13. Zbl 0723.05047, MR 1040769 |
| Reference:
|
[5] MacGillivray, G., Tifenbach, R. M., Driessche, P. van den: Spectrally arbitrary star sign patterns.Linear Algebra Appl. 400 (2005), 99-119. MR 2131919 |
| Reference:
|
[6] Yeh, L.: Sign pattern matrices that allow a nilpotent matrix.Bull. Aust. Math. Soc. 53 (1996), 189-196. Zbl 0848.15014, MR 1381760, 10.1017/S0004972700016907 |
| . |
