| Title:
|
Symmetric sign patterns with maximal inertias (English) |
| Author:
|
Kim, In-Jae |
| Author:
|
Waters, Charles |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
101-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The inertia of an $n$ by $n$ symmetric sign pattern is called maximal when it is not a proper subset of the inertia of another symmetric sign pattern of order $n$. In this note we classify all the maximal inertias for symmetric sign patterns of order $n$, and identify symmetric sign patterns with maximal inertias by using a rank-one perturbation. (English) |
| Keyword:
|
eigenvalue |
| Keyword:
|
inertia |
| Keyword:
|
maximal inertia |
| Keyword:
|
rank-one perturbation |
| Keyword:
|
symmetric sign pattern |
| MSC:
|
15A18 |
| MSC:
|
15B35 |
| idZBL:
|
Zbl 1224.15061 |
| idMR:
|
MR2595074 |
| . |
| Date available:
|
2010-07-20T16:17:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140553 |
| . |
| Reference:
|
[1] Cavers, M. S., Meulen, K. N. Vander: Spectrally and inertially arbitrary sign patterns.Linear Algebra Appl. 394 (2005), 53-72. MR 2100576 |
| Reference:
|
[2] Fonseca, C. M. da: On the inertia sets of some symmetric sign patterns.Czechoslovak Math. J. 56 (2006), 875-883. Zbl 1164.15318, MR 2261659, 10.1007/s10587-006-0062-0 |
| Reference:
|
[3] Gao, Y., Shao, Y.: The inertia set of nonnegative symmetric sign pattern with zero diagonal.Czechoslovak Math. J. 53 (2003), 925-934. Zbl 1080.15501, MR 2018840, 10.1023/B:CMAJ.0000024531.10708.9f |
| Reference:
|
[4] Horn, R. A., Johnson, C. R.: Matrix Analysis.Cambridge Univeristy Press Cambridge (1985). Zbl 0576.15001, MR 0832183 |
| Reference:
|
[5] Hall, F. J., Li, Z.: Inertia sets of symmetric sign pattern matrices.Numer. Math., J. Chin. Univ. (English Ser.) 10 (2001), 226-240. Zbl 0997.15010, MR 1884971 |
| Reference:
|
[6] Hall, F. J., Li, Z., Wang, Di: Symmetric sign pattern matrices that require unique inertia.Linear Algebra Appl. 338 (2001), 153-169. Zbl 0994.15028, MR 1861120 |
| Reference:
|
[7] Hall, F. J., Li, Z., Wang, Di: Symmetric sign pattern matrices that require unique inertia.Linear Algebra Appl. 338 (2001), 153-169. Zbl 0994.15028, MR 1861120 |
| . |
