{"title":"The values of the generalized matrix functions of 3 × 3 matrices","authors":"R. Tabata","doi":"10.32917/HMJ/1428365051","DOIUrl":null,"url":null,"abstract":"When A is a 3 × 3 positive semi-definite Hermitian matrix, Schur’s inequality and the permanental dominance conjecture are known to hold. In [5], we determined the possible positions of the normalized generalized matrix functions relative to the determinant and the permanent except in the case that the order of the subgroup is 2. The purpose of this paper is to determine the possible positions in the last open case.","PeriodicalId":55054,"journal":{"name":"Hiroshima Mathematical Journal","volume":"45 1","pages":"1-8"},"PeriodicalIF":0.5000,"publicationDate":"2015-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hiroshima Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.32917/HMJ/1428365051","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
When A is a 3 × 3 positive semi-definite Hermitian matrix, Schur’s inequality and the permanental dominance conjecture are known to hold. In [5], we determined the possible positions of the normalized generalized matrix functions relative to the determinant and the permanent except in the case that the order of the subgroup is 2. The purpose of this paper is to determine the possible positions in the last open case.
期刊介绍:
Hiroshima Mathematical Journal (HMJ) is a continuation of Journal of Science of the Hiroshima University, Series A, Vol. 1 - 24 (1930 - 1960), and Journal of Science of the Hiroshima University, Series A - I , Vol. 25 - 34 (1961 - 1970).
Starting with Volume 4 (1974), each volume of HMJ consists of three numbers annually. This journal publishes original papers in pure and applied mathematics. HMJ is an (electronically) open access journal from Volume 36, Number 1.