| Title:
|
Perimeter preserver of matrices over semifields (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:
|
2 |
| Year:
|
2006 |
| Pages:
|
515-524 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a rank-$1$ matrix $A= {\bold a \bold b}^t$, we define the perimeter of $A$ as the number of nonzero entries in both $\bold a$ and $\bold b$. We characterize the linear operators which preserve the rank and perimeter of rank-$1$ matrices over semifields. That is, a linear operator $T$ preserves the rank and perimeter of rank-$1$ matrices over semifields if and only if it has the form $T(A)=U A V$, or $T(A)=U A^t V$ with some invertible matrices U and V. (English) |
| Keyword:
|
linear operator |
| Keyword:
|
rank |
| Keyword:
|
dominate |
| Keyword:
|
perimeter |
| Keyword:
|
$(U,V)$-operator |
| MSC:
|
15A03 |
| MSC:
|
15A04 |
| MSC:
|
15A23 |
| MSC:
|
15A33 |
| idZBL:
|
Zbl 1164.15300 |
| idMR:
|
MR2291752 |
| . |
| Date available:
|
2009-09-24T11:35:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128082 |
| . |
| Reference:
|
[1] L. B. Beasley and N. J. Pullman: Boolean rank-preserving operators and Boolean rank-1 spaces.Linear Algebra Appl. 59 (1984), 55–77. MR 0743045, 10.1016/0024-3795(84)90158-7 |
| 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] S. Z. Song, S. R. Park: Maximal column rank preservers of fuzzy matrices.Discuss. Math. Gen. Algebra Appl. 21 (2001), 207–218. MR 1894316, 10.7151/dmgaa.1038 |
| . |
