{"title":"关于矩阵有限确定性的一个注记","authors":"Thuy Huong Pham, P. Marques","doi":"10.4310/pamq.2020.v16.n4.a10","DOIUrl":null,"url":null,"abstract":"In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by change of coordinates together with multiplication by invertible matrices from both sides.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"81 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A note on finite determinacy of matrices\",\"authors\":\"Thuy Huong Pham, P. Marques\",\"doi\":\"10.4310/pamq.2020.v16.n4.a10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by change of coordinates together with multiplication by invertible matrices from both sides.\",\"PeriodicalId\":278201,\"journal\":{\"name\":\"arXiv: Algebraic Geometry\",\"volume\":\"81 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2020.v16.n4.a10\",\"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: Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/pamq.2020.v16.n4.a10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by change of coordinates together with multiplication by invertible matrices from both sides.