| Title:
|
Invertible commutativity preservers of matrices over max algebra (English) |
| Author:
|
Song, Seok-Zun |
| Author:
|
Kang, Kyung-Tae |
| Author:
|
Jun, Young-Bae |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
1185-1192 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We characterize the invertible linear operators that preserve the set of commuting pairs of matrices over a subalgebra of max algebra. (English) |
| Keyword:
|
max algebra |
| Keyword:
|
linear operator |
| Keyword:
|
pair of commuting matrices |
| MSC:
|
15A03 |
| MSC:
|
15A04 |
| MSC:
|
15A27 |
| MSC:
|
15A33 |
| idZBL:
|
Zbl 1164.15303 |
| idMR:
|
MR2280802 |
| . |
| Date available:
|
2009-09-24T11:42:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128138 |
| . |
| Reference:
|
[1] L. B. Beasley: Linear transformations on matrices: the invariance of commuting pairs of matrices.Linear and Multilinear Algebra 6 (1978), 179–183. Zbl 0397.15010, MR 0512993, 10.1080/03081087808817236 |
| Reference:
|
[2] L. B. Beasley and N. J. Pullman: Linear operators that strongly preserve commuting pairs of fuzzy matrices.Fuzzy Sets and Systems 41 (1991), 167–173. MR 1111964, 10.1016/0165-0114(91)90220-K |
| Reference:
|
[3] P. Moller: Theorie algebrique des Systemes a Evenements Discrets.These, Ecole des Mines de Paris, 1988. |
| Reference:
|
[4] S. Z. Song and K. T. Kang: Column ranks and their preservers of matrices over max algebra.Linear and Multilinear Algebra 51 (2003), 311–318. MR 1995662, 10.1080/0308108031000069173 |
| Reference:
|
[5] W. Watkins: Linear maps that preserve commuting pairs of matrices.Linear Algebra and Appl. 14 (1976), 29–35. Zbl 0329.15005, MR 0480574, 10.1016/0024-3795(76)90060-4 |
| . |
