On upper triangular nonnegative matrices

Chen, Yizhi, Zhao, Xian Zhong, and Liu, Zhongzhu. "On upper triangular nonnegative matrices." Czechoslovak Mathematical Journal 65.1 (2015): 1-20. <http://eudml.org/doc/270031>.

@article{Chen2015,
abstract = {We first investigate factorizations of elements of the semigroup $S$ of upper triangular matrices with nonnegative entries and nonzero determinant, provide a formula for $\rho (S)$, and, given $A\in S$, also provide formulas for $l(A)$, $L(A)$ and $\rho (A)$. As a consequence, open problem 2 and problem 4 presented in N. Baeth et al. (2011), are partly answered. Secondly, we study the semigroup of upper triangular matrices with only positive integral entries, compute some invariants of such semigroup, and also partly answer open Problem 1 and Problem 3 in N. Baeth et al. (2011).},
author = {Chen, Yizhi, Zhao, Xian Zhong, Liu, Zhongzhu},
journal = {Czechoslovak Mathematical Journal},
keywords = {upper triangular; nonnegative matrix; factorization; matrix semigroup; upper triangular; nonnegative matrix; factorization; matrix semigroup},
language = {eng},
number = {1},
pages = {1-20},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On upper triangular nonnegative matrices},
url = {http://eudml.org/doc/270031},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Chen, Yizhi
AU - Zhao, Xian Zhong
AU - Liu, Zhongzhu
TI - On upper triangular nonnegative matrices
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 1
EP - 20
AB - We first investigate factorizations of elements of the semigroup $S$ of upper triangular matrices with nonnegative entries and nonzero determinant, provide a formula for $\rho (S)$, and, given $A\in S$, also provide formulas for $l(A)$, $L(A)$ and $\rho (A)$. As a consequence, open problem 2 and problem 4 presented in N. Baeth et al. (2011), are partly answered. Secondly, we study the semigroup of upper triangular matrices with only positive integral entries, compute some invariants of such semigroup, and also partly answer open Problem 1 and Problem 3 in N. Baeth et al. (2011).
LA - eng
KW - upper triangular; nonnegative matrix; factorization; matrix semigroup; upper triangular; nonnegative matrix; factorization; matrix semigroup
UR - http://eudml.org/doc/270031
ER -