{"title":"连续矩阵定理--行列式的性质","authors":"Pablo Roberto Dias","doi":"10.37418/amsj.12.12.1","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to present the proof that the determinant of any matrix of order higher than 2 ($k > 2$) where elements are consecutive numbers or numbers following an arithmetic progression will always be zero.","PeriodicalId":231117,"journal":{"name":"Advances in Mathematics: Scientific Journal","volume":"20 5","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"THE CONSECUTIVE MATRIX THEOREM - A PROPERTY OF DETERMINANTS\",\"authors\":\"Pablo Roberto Dias\",\"doi\":\"10.37418/amsj.12.12.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to present the proof that the determinant of any matrix of order higher than 2 ($k > 2$) where elements are consecutive numbers or numbers following an arithmetic progression will always be zero.\",\"PeriodicalId\":231117,\"journal\":{\"name\":\"Advances in Mathematics: Scientific Journal\",\"volume\":\"20 5\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics: Scientific Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37418/amsj.12.12.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematics: Scientific Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37418/amsj.12.12.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
THE CONSECUTIVE MATRIX THEOREM - A PROPERTY OF DETERMINANTS
The purpose of this paper is to present the proof that the determinant of any matrix of order higher than 2 ($k > 2$) where elements are consecutive numbers or numbers following an arithmetic progression will always be zero.
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