| Title:
|
Perimeter preservers of nonnegative integer matrices (English) |
| Author:
|
Song, Seok-Zun |
| Author:
|
Kang, Kyung-Tae |
| Author:
|
Yi, Sucheol |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
9-15 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the perimeter of nonnegative integer matrices. We also characterize the linear operators which preserve the rank and perimeter of nonnegative integer matrices. That is, a linear operator $T$ preserves the rank and perimeter of rank-$1$ matrices if and only if it has the form $T(A)=P(A\circ B)Q$, or $T(A)=P(A^t \circ B)Q $ with appropriate permutation matrices $P$ and $Q$ and positive integer matrix $B$, where $\circ$ denotes Hadamard product. (English) |
| Keyword:
|
linear operator |
| Keyword:
|
rank |
| Keyword:
|
perimeter |
| Keyword:
|
$(P, Q, B)$-operator |
| MSC:
|
15A04 |
| MSC:
|
15A30 |
| MSC:
|
15A33 |
| MSC:
|
15A36 |
| MSC:
|
15A48 |
| idZBL:
|
Zbl 1099.15001 |
| idMR:
|
MR2076857 |
| . |
| Date available:
|
2009-05-05T16:43:01Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119434 |
| . |
| Reference:
|
[1] Beasley L.B., Pullman N.J.: Boolean rank-preserving operators and Boolean rank-$1$ spaces.Linear Algebra Appl. 59 (1984), 55-77. Zbl 0536.20044, MR 0743045 |
| Reference:
|
[2] Beasley L.B., Gregory D.A., Pullman N.J.: Nonnegative rank-preserving operators.Linear Algebra Appl. 65 (1985), 207-223. Zbl 0561.15002, MR 0774353 |
| Reference:
|
[3] Beasley L.B., Pullman N.J.: Term-rank, permanent and rook-polynomial preservers.Linear Algebra Appl. 90 (1987), 33-46. Zbl 0617.15001, MR 0884107 |
| Reference:
|
[4] Beasley L.B., Song S.Z., Lee S.G.: Zero term rank preservers.Linear and Multilinear Algebra 48 (2001), 313-318. Zbl 0987.15002, MR 1928400 |
| Reference:
|
[5] Song S.Z.: Linear operators that preserve maximal column ranks of nonnegative integer matrices.Proc. Amer. Math. Soc. 126 (1998), 2205-2211. Zbl 0896.15009, MR 1443409 |
| . |
