| Title:
|
On the inertia sets of some symmetric sign patterns (English) |
| Author:
|
Fonseca, C. M. da |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
875-883 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A matrix whose entries consist of elements from the set $\lbrace +,-,0\rbrace $ is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices. (English) |
| Keyword:
|
inertia |
| Keyword:
|
sign pattern matrix |
| Keyword:
|
tridiagonal matrix |
| MSC:
|
15A18 |
| MSC:
|
15A36 |
| MSC:
|
15A48 |
| idZBL:
|
Zbl 1164.15318 |
| idMR:
|
MR2261659 |
| . |
| Date available:
|
2009-09-24T11:38:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128112 |
| . |
| Reference:
|
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| Reference:
|
[2] B. E. Cain and E. Marques de Sá: The inertia of certain skew-triangular block matrices.Linear Algebra Appl. 160 (1992), 75–85. MR 1137844 |
| Reference:
|
[3] C. Eschenbach and C. R. Johnson: A combinatorial converse to the Perron-Frobenius theorem.Linear Algebra Appl. 136 (1990), 173–180. MR 1061544 |
| Reference:
|
[4] C. Eschenbach and C. R. Johnson: Sign patterns that require real, nonreal or pure imaginary eigenvalues.Linear and Multilinear Algebra 29 (1991), 299–311. MR 1119461, 10.1080/03081089108818079 |
| Reference:
|
[5] Y. Gao and Y. Shao: The inertia set of nonnegative symmetric sign pattern with zero diagonal.Czechoslovak Math. J. 53 (2003), 925–934. MR 2018840, 10.1023/B:CMAJ.0000024531.10708.9f |
| Reference:
|
[6] F. J. Hall and Z. Li: Inertia sets of symmetric sign pattern matrices.Numer. Math. J. Chinese Univ. (English Ser.) 10 (2001), 226–240. MR 1884971 |
| Reference:
|
[7] F. J. Hall, Z. Li and Di Wang: Symmetric sign pattern matrices that require unique inertia.Linear Algebra Appl. 338 (2001), 153–169. MR 1861120 |
| Reference:
|
[8] R. A. Horn and C. R. Johnson: Matrix Analysis, Cambridge University Press, Cambridge.1985. MR 0832183 |
| Reference:
|
[9] C. Jeffries and C. R. Johnson: Some sign patterns that preclude matrix stability.SIAM J. Matrix Anal. Appl. 9 (1988), 19–25. MR 0938055 |
| . |
