Geodesic
On upper triangular nonnegative matrices
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 1-20.

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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).
DOI : 10.1007/s10587-015-0158-5
Classification : 11Y05, 15A23
Keywords: upper triangular; nonnegative matrix; factorization; matrix semigroup 
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Chen, Yizhi; Zhao, Xianzhong; Liu, Zhongzhu. On upper triangular nonnegative matrices. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 1-20. doi : 10.1007/s10587-015-0158-5. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0158-5/

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