| Title:
|
Extreme preservers of maximal column rank inequalities of matrix sums over semirings (English) |
| Author:
|
Song, Seok-Zun |
| Author:
|
Park, Kwon-Ryong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
693-703 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize linear operators that preserve sets of matrix ordered pairs which satisfy extreme properties with respect to maximal column rank inequalities of matrix sums over semirings. (English) |
| Keyword:
|
linear operator |
| Keyword:
|
rank inequality |
| Keyword:
|
maximal column rank. |
| MSC:
|
15A03 |
| MSC:
|
15A04 |
| MSC:
|
15A45 |
| idZBL:
|
Zbl 1174.15001 |
| idMR:
|
MR2455931 |
| . |
| Date available:
|
2010-07-20T13:59:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140414 |
| . |
| Reference:
|
[1] Beasley, L. B., Guterman, A. E.: Rank inequalities over semirings.J. Korean Math. Soc. 42 (2005), 223-241. Zbl 1127.15001, MR 2121497, 10.4134/JKMS.2005.42.2.223 |
| Reference:
|
[2] Beasley, L. B., Guterman, A. E.: Linear preservers of extremes of rank inequalities over semirings: Factor rank.J. Math. Sci., New York 131 (2005), 5919-5938. MR 2153693, 10.1007/s10958-005-0451-1 |
| Reference:
|
[3] Beasley, L. B., Guterman, A. E., Neal, C. L.: Linear preservers for Sylvester and Frobenius bounds on matrix rank.Rocky Mt. J. Math. 36 (2006), 67-80. Zbl 1134.15003, MR 2228184, 10.1216/rmjm/1181069488 |
| Reference:
|
[4] Beasley, L. B., Lee, S.-G., Song, S.-Z.: Linear operators that preserve pairs of matrices which satisfy extreme rank properties.Linear Algebra Appl. 350 (2002), 263-272. Zbl 1004.15025, MR 1906757 |
| Reference:
|
[5] Beasley, L. B., Pullman, N. J.: Semiring rank versus column rank.Linear Algebra Appl. 101 (1988), 33-48. Zbl 0642.15002, MR 0941294 |
| Reference:
|
[6] Guterman, A. E.: Linear preservers for matrix inequalities and partial orderings.Linear Algebra Appl. 331 (2001), 75-87. Zbl 0985.15018, MR 1832488 |
| Reference:
|
[7] Marsaglia, G., Styan, P.: When does $\operatorname{rank}(A+B)=\operatorname{rank}(A)+\operatorname{rank}(B)$?.Canad. Math. Bull. 15 (1972), 451-452. MR 0311674, 10.4153/CMB-1972-082-8 |
| Reference:
|
[8] al., P. Pierce at: A survey of linear preserver problems.Linear Multilinear Algebra 33 (1992), 1-119. 10.1080/03081089208818176 |
| Reference:
|
[9] Song, S.-Z.: Linear operators that preserve maximal column ranks of nonnegative integer matrices.Proc. Am. Math. Soc. 126 (1998), 2205-2211. Zbl 0896.15009, MR 1443409, 10.1090/S0002-9939-98-04308-1 |
| . |
