Factorization of a prime matrix in even blocks
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929446025428992 |
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| author | Wang, Haoming |
| author_facet | Wang, Haoming |
| contents | In this paper, a matrix is said to be prime if the row and column of this matrix are both prime numbers. We establish various necessary and sufficient conditions for developing matrices into the sum of tensor products of prime matrices. For example, if the diagonal of a matrix blocked evenly are pairwise commutative, it yields such a decomposition. The computational complexity of multiplication of these algorithms is shown to be $O(n^{5/2})$. In the section 5, a decomposition is proved to hold if and only if every even natural number greater than 2 is the sum of two prime numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00627 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Factorization of a prime matrix in even blocks Wang, Haoming Numerical Analysis Optimization and Control Rings and Algebras 11A51, 15A69, 15A99 In this paper, a matrix is said to be prime if the row and column of this matrix are both prime numbers. We establish various necessary and sufficient conditions for developing matrices into the sum of tensor products of prime matrices. For example, if the diagonal of a matrix blocked evenly are pairwise commutative, it yields such a decomposition. The computational complexity of multiplication of these algorithms is shown to be $O(n^{5/2})$. In the section 5, a decomposition is proved to hold if and only if every even natural number greater than 2 is the sum of two prime numbers. |
| title | Factorization of a prime matrix in even blocks |
| topic | Numerical Analysis Optimization and Control Rings and Algebras 11A51, 15A69, 15A99 |
| url | https://arxiv.org/abs/2408.00627 |