{"title":"素数矩阵的偶数块因式分解","authors":"Haoming Wang","doi":"arxiv-2408.00627","DOIUrl":null,"url":null,"abstract":"In this paper, a matrix is said to be prime if the row and column of this\nmatrix are both prime numbers. We establish various necessary and sufficient\nconditions for developing matrices into the sum of tensor products of prime\nmatrices. For example, if the diagonal of a matrix blocked evenly are pairwise\ncommutative, it yields such a decomposition. The computational complexity of\nmultiplication of these algorithms is shown to be $O(n^{5/2})$. In the section\n5, a decomposition is proved to hold if and only if every even natural number\ngreater than 2 is the sum of two prime numbers.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Factorization of a prime matrix in even blocks\",\"authors\":\"Haoming Wang\",\"doi\":\"arxiv-2408.00627\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, a matrix is said to be prime if the row and column of this\\nmatrix are both prime numbers. We establish various necessary and sufficient\\nconditions for developing matrices into the sum of tensor products of prime\\nmatrices. For example, if the diagonal of a matrix blocked evenly are pairwise\\ncommutative, it yields such a decomposition. The computational complexity of\\nmultiplication of these algorithms is shown to be $O(n^{5/2})$. In the section\\n5, a decomposition is proved to hold if and only if every even natural number\\ngreater than 2 is the sum of two prime numbers.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.00627\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.00627","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.