On Factorizations of Upper Triangular Nonnegative Matrices of Order Three
Let T3(N0) denote the semigroup of 3×3 upper triangular matrices with nonnegative integral-valued entries. In this paper, we investigate factorizations of upper triangular nonnegative matrices of order three. Firstly, we characterize the atoms of the subsemigroup S of the matrices in T3(N0) with non...
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Hindawi Limited
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/960182 |
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doaj-d26fedaf7a3549f59dc67647fbd40d9b2020-11-24T21:20:10ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/960182960182On Factorizations of Upper Triangular Nonnegative Matrices of Order ThreeYi-Zhi Chen0Department of Mathematics, Huizhou University, Huizhou, Guangdong 516007, ChinaLet T3(N0) denote the semigroup of 3×3 upper triangular matrices with nonnegative integral-valued entries. In this paper, we investigate factorizations of upper triangular nonnegative matrices of order three. Firstly, we characterize the atoms of the subsemigroup S of the matrices in T3(N0) with nonzero determinant and give some formulas. As a consequence, problems 4a and 4c presented by Baeth et al. (2011) are each half-answered for the case n=3. And then, we consider some factorization cases of matrix A in S with ρ(A)=1 and give formulas for the minimum factorization length of some special matrices in S.http://dx.doi.org/10.1155/2015/960182 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yi-Zhi Chen |
| spellingShingle |
Yi-Zhi Chen On Factorizations of Upper Triangular Nonnegative Matrices of Order Three Discrete Dynamics in Nature and Society |
| author_facet |
Yi-Zhi Chen |
| author_sort |
Yi-Zhi Chen |
| title |
On Factorizations of Upper Triangular Nonnegative Matrices of Order Three |
| title_short |
On Factorizations of Upper Triangular Nonnegative Matrices of Order Three |
| title_full |
On Factorizations of Upper Triangular Nonnegative Matrices of Order Three |
| title_fullStr |
On Factorizations of Upper Triangular Nonnegative Matrices of Order Three |
| title_full_unstemmed |
On Factorizations of Upper Triangular Nonnegative Matrices of Order Three |
| title_sort |
on factorizations of upper triangular nonnegative matrices of order three |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1026-0226 1607-887X |
| publishDate |
2015-01-01 |
| description |
Let T3(N0) denote the semigroup of 3×3 upper triangular matrices with nonnegative integral-valued entries. In this paper, we investigate factorizations of upper triangular nonnegative matrices of order three. Firstly, we characterize the atoms of the subsemigroup S of the matrices in T3(N0) with nonzero determinant and give some formulas. As a consequence, problems 4a and 4c presented by Baeth et al. (2011) are each half-answered for the case n=3. And then, we consider some factorization cases of matrix A in S with ρ(A)=1 and give formulas for the minimum factorization length of some special matrices in S. |
| url |
http://dx.doi.org/10.1155/2015/960182 |
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AT yizhichen onfactorizationsofuppertriangularnonnegativematricesoforderthree |
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