{"title":"双随机矩阵的一个不等式","authors":"Charles R. Johnson, R. Kellogg","doi":"10.6028/JRES.080B.046","DOIUrl":null,"url":null,"abstract":"Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x\" :0:::; YIY\" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron· Frobenius eigenvalue of A. The relationship between these two inequalities is exhibited.","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"67 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1976-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"An inequality for doubly stochastic matrices\",\"authors\":\"Charles R. Johnson, R. Kellogg\",\"doi\":\"10.6028/JRES.080B.046\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x\\\" :0:::; YIY\\\" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron· Frobenius eigenvalue of A. The relationship between these two inequalities is exhibited.\",\"PeriodicalId\":166823,\"journal\":{\"name\":\"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences\",\"volume\":\"67 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1976-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6028/JRES.080B.046\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/JRES.080B.046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x" :0:::; YIY" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron· Frobenius eigenvalue of A. The relationship between these two inequalities is exhibited.
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