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On upper triangular nonnegative matrices

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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 ϱ(S), and, given A ∈ S, also provide formulas for l(A), L(A) and ϱ(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).

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Authors and Affiliations

  1. Department of Mathematics, Huizhou University, Huizhou, Guangdong, 516007, P.R. China

    Yizhi Chen & Zhongzhu Liu

  2. College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P.R. China

    Xianzhong Zhao

Authors
  1. Yizhi Chen
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  2. Xianzhong Zhao
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  3. Zhongzhu Liu
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Corresponding author

Correspondence to Yizhi Chen.

Additional information

This paper was supported by National Natural Science Foundation of China (11401246, 11426112); Natural Science Foundation of Guangdong Province (2014A030310087, 2014A030310119); Natural Science Foundation of Fujian Province (2014J01019); Outstanding Young Innovative Talent Training Project in Guangdong Universities (2013LYM0086); Science Technology Plan Project of Huizhou City.

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Chen, Y., Zhao, X. & Liu, Z. On upper triangular nonnegative matrices. Czech Math J 65, 1–20 (2015). https://doi.org/10.1007/s10587-015-0158-5

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  • DOI: https://doi.org/10.1007/s10587-015-0158-5

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