Perimeter preserver of matrices over semifields

Song, Seok-Zun, Kang, Kyung-Tae, and Jun, Young Bae. "Perimeter preserver of matrices over semifields." Czechoslovak Mathematical Journal 56.2 (2006): 515-524. <http://eudml.org/doc/31044>.

@article{Song2006,
abstract = {For a rank-$1$ matrix $A= \{\mathbf \{a\} \mathbf \{b\}\}^t$, we define the perimeter of $A$ as the number of nonzero entries in both $\mathbf \{a\}$ and $\mathbf \{b\}$. 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.},
author = {Song, Seok-Zun, Kang, Kyung-Tae, Jun, Young Bae},
journal = {Czechoslovak Mathematical Journal},
keywords = {linear operator; rank; dominate; perimeter; $(U,V)$-operator; linear operator; rank; dominate; perimeter; -operator; perimeter preserver; rank preserver},
language = {eng},
number = {2},
pages = {515-524},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Perimeter preserver of matrices over semifields},
url = {http://eudml.org/doc/31044},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Song, Seok-Zun
AU - Kang, Kyung-Tae
AU - Jun, Young Bae
TI - Perimeter preserver of matrices over semifields
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 515
EP - 524
AB - For a rank-$1$ matrix $A= {\mathbf {a} \mathbf {b}}^t$, we define the perimeter of $A$ as the number of nonzero entries in both $\mathbf {a}$ and $\mathbf {b}$. 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.
LA - eng
KW - linear operator; rank; dominate; perimeter; $(U,V)$-operator; linear operator; rank; dominate; perimeter; -operator; perimeter preserver; rank preserver
UR - http://eudml.org/doc/31044
ER -