| Title:
|
Zero-term ranks of real matrices and their preservers (English) |
| Author:
|
Beasley, LeRoy B. |
| Author:
|
Jun, Young-Bae |
| Author:
|
Song, Seok-Zun |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
183-188 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve zero-term rank of the $m \times n$ real matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix. (English) |
| Keyword:
|
linear operator |
| Keyword:
|
zero-term rank |
| Keyword:
|
$P,Q,B$-operator |
| MSC:
|
15A03 |
| MSC:
|
15A04 |
| idZBL:
|
Zbl 1051.15001 |
| idMR:
|
MR2040230 |
| . |
| Date available:
|
2009-09-24T11:11:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127875 |
| . |
| Reference:
|
[1] L. B. Beasley and N. J. Pullman: Term-rank, permanent and rook-polynomial preservers.Linear Algebra Appl. 90 (1987), 33–46. MR 0884107, 10.1016/0024-3795(87)90302-8 |
| Reference:
|
[2] L. B. Beasley, S. Z. Song and S. G. Lee: Zero-term rank preservers.Linear and Multilinear Algebra 48 (2001), 313–318. MR 1928400, 10.1080/03081080108818677 |
| Reference:
|
[3] C. R. Johnson and J. S. Maybee: Vanishing minor conditions for inverse zero patterns.Linear Algebra Appl. 178 (1993), 1–15. MR 1197498 |
| . |
