| Title:
|
$\pm$ sign pattern matrices that allow orthogonality (English) |
| Author:
|
Shao, Yanling |
| Author:
|
Sun, Liang |
| Author:
|
Gao, Yubin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
969-979 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A sign pattern $A$ is a $\pm $ sign pattern if $A$ has no zero entries. $A$ allows orthogonality if there exists a real orthogonal matrix $B$ whose sign pattern equals $A$. Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for $\pm $ sign patterns with $n-1 \le N_-(A) \le n+1$ to allow orthogonality. (English) |
| Keyword:
|
sign pattern |
| Keyword:
|
orthogonality |
| Keyword:
|
orthogonal matrix |
| MSC:
|
15A18 |
| MSC:
|
15A36 |
| MSC:
|
15A48 |
| MSC:
|
15A99 |
| idZBL:
|
Zbl 1164.15327 |
| idMR:
|
MR2261669 |
| . |
| Date available:
|
2009-09-24T11:40:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128122 |
| . |
| Reference:
|
[1] L. B. Beasley, R. A. Brualdi, and B. L. Shader: Combinatorial orthogonality.In: Combinatorial and Graph-Theoretical Problems in Linear Algebra, R. A. Brualdi, S. Friedland, and V. Klee (eds.), Springer-Verlag, Berlin, 1993, pp. 207–218. MR 1240965 |
| Reference:
|
[2] G.-S. Cheon, B. L. Shader: How sparse can a matrix with orthogonal rows be?.Journal of Combinatorial Theory, Series A 85 (1999), 29–40. MR 1659464, 10.1006/jcta.1998.2898 |
| Reference:
|
[3] C. Waters: Sign pattern matrices that allow orthogonality.Linear Algebra Appl. 235 (1996), 1–16. Zbl 0852.15018, MR 1374247 |
| Reference:
|
[4] G.-S. Cheon, C. R. Johnson, S.-G. Lee, and E. J. Pribble: The possible numbers of zeros in an orthogonal matrix.Electron. J. Linear Algebra 5 (1999), 19–23. MR 1659324 |
| Reference:
|
[5] C. A. Eschenbach, F. J. Hall, D. L. Harrell, and Z. Li: When does the inverse have the same pattern as the transpose?.Czechoslovak Math. J. 124 (1999), 255–275. MR 1692477, 10.1023/A:1022496101277 |
| Reference:
|
[6] R. A. Horn, C. R. Johnson: Matrix Analysis.Cambridge University Press, Cambridge, 1985. MR 0832183 |
| . |
