| Title:
|
The inertia set of nonnegative symmetric sign pattern with zero diagonal (English) |
| Author:
|
Gao, Yubin |
| Author:
|
Shao, Yanling |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
925-934 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The inertia set of a symmetric sign pattern $A$ is the set $i(A)=\lbrace i(B) \mid B=B^T \in Q(A)\rbrace $, where $i(B)$ denotes the inertia of real symmetric matrix $B$, and $Q(A)$ denotes the sign pattern class of $A$. In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern $A$ in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns $A$ with zero diagonal that require unique inertia. (English) |
| Keyword:
|
sign pattern |
| Keyword:
|
inertia |
| Keyword:
|
inertia set |
| Keyword:
|
unique inertia |
| MSC:
|
15A18 |
| idZBL:
|
Zbl 1080.15501 |
| idMR:
|
MR2018840 |
| . |
| Date available:
|
2009-09-24T11:07:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127850 |
| . |
| Reference:
|
[1] B. N. Datta: Stability and inertia.Linear Algebra Appl. 302–303 (1999), 563–600. Zbl 0972.15009, MR 1733550 |
| Reference:
|
[2] J. H. Drew, C. R. Johnson, D. D. Olesky and P. van den Driessche: Spectrally arbitrary patterns.Linear Algebra Appl. 308 (2000), 121–137. MR 1751135 |
| Reference:
|
[3] R. A. Horn and C. R. Johnson: Matrix Analysis.Cambridge University Press, Cambridge, 1985. MR 0832183 |
| Reference:
|
[4] R. A. Brualdi and B. L. Shader: Matrices of Sign-solvable Linear System.Cambridge University Press, Cambridge, 1995. MR 1358133 |
| . |
