Some properties of n-matrix factorizations of polynomials
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915142398115840 |
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| author | Fomatati, Yves |
| author_facet | Fomatati, Yves |
| contents | Let $R=K[x_{1},x_{2},\cdots, x_{m}]$ where $K$ is a field. In this paper, we give some properties of $n$-matrix factorizations of polynomials in $R$. We also derive some results giving some lower bounds on the number of $n$-matrix factors of polynomials. In particular, we give a lower bound on the number of matrix factors of minimal size for the sums of squares polynomial $f_{m}=x_{1}^{2}+\cdots + x_{m}^{2}$ for $m=8$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03372 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some properties of n-matrix factorizations of polynomials Fomatati, Yves Rings and Algebras 15A23, 12D05, 16D40 Let $R=K[x_{1},x_{2},\cdots, x_{m}]$ where $K$ is a field. In this paper, we give some properties of $n$-matrix factorizations of polynomials in $R$. We also derive some results giving some lower bounds on the number of $n$-matrix factors of polynomials. In particular, we give a lower bound on the number of matrix factors of minimal size for the sums of squares polynomial $f_{m}=x_{1}^{2}+\cdots + x_{m}^{2}$ for $m=8$. |
| title | Some properties of n-matrix factorizations of polynomials |
| topic | Rings and Algebras 15A23, 12D05, 16D40 |
| url | https://arxiv.org/abs/2310.03372 |