Perimeter preservers of nonnegative integer matrices
Seok-Zun Song; Kyung-Tae Kang; Sucheol Yi
Commentationes Mathematicae Universitatis Carolinae (2004)
- Volume: 45, Issue: 1, page 9-15
- ISSN: 0010-2628
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topSong, Seok-Zun, Kang, Kyung-Tae, and Yi, Sucheol. "Perimeter preservers of nonnegative integer matrices." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 9-15. <http://eudml.org/doc/249326>.
@article{Song2004,
abstract = {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.},
author = {Song, Seok-Zun, Kang, Kyung-Tae, Yi, Sucheol},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear operator; rank; perimeter; $(P, Q, B)$-operator; nonnegative matrices; rank preserver; perimeter preserver; linear operator; integer matrices},
language = {eng},
number = {1},
pages = {9-15},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Perimeter preservers of nonnegative integer matrices},
url = {http://eudml.org/doc/249326},
volume = {45},
year = {2004},
}
TY - JOUR
AU - Song, Seok-Zun
AU - Kang, Kyung-Tae
AU - Yi, Sucheol
TI - Perimeter preservers of nonnegative integer matrices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 9
EP - 15
AB - 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.
LA - eng
KW - linear operator; rank; perimeter; $(P, Q, B)$-operator; nonnegative matrices; rank preserver; perimeter preserver; linear operator; integer matrices
UR - http://eudml.org/doc/249326
ER -
References
top- Beasley L.B., Pullman N.J., Boolean rank-preserving operators and Boolean rank- spaces, Linear Algebra Appl. 59 (1984), 55-77. (1984) Zbl0536.20044MR0743045
- Beasley L.B., Gregory D.A., Pullman N.J., Nonnegative rank-preserving operators, Linear Algebra Appl. 65 (1985), 207-223. (1985) Zbl0561.15002MR0774353
- Beasley L.B., Pullman N.J., Term-rank, permanent and rook-polynomial preservers, Linear Algebra Appl. 90 (1987), 33-46. (1987) Zbl0617.15001MR0884107
- Beasley L.B., Song S.Z., Lee S.G., Zero term rank preservers, Linear and Multilinear Algebra 48 (2001), 313-318. (2001) Zbl0987.15002MR1928400
- Song S.Z., Linear operators that preserve maximal column ranks of nonnegative integer matrices, Proc. Amer. Math. Soc. 126 (1998), 2205-2211. (1998) Zbl0896.15009MR1443409
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