文章摘要
引用本文:林志兴,杨忠鹏,陈梅香,陈智雄.和与积相等的Hermitian矩阵对的惯性及应用[J].福州大学学报(自然科学版),2018,46(1):27~31
和与积相等的Hermitian矩阵对的惯性及应用
Inertia of Hermitian matrix pairs whose sum is equal to its product and its applications
  
DOI:10.7631/issn.1000-2243.16378
中文关键词: Hermitian矩阵  惯性  矩阵方程  
英文关键词: Hermitian matrix  inertia  matrix equation  rank of matrix
基金项目:
作者单位
林志兴 莆田学院数学与金融学院福建 莆田 351100 
杨忠鹏 莆田学院数学与金融学院福建 莆田 351100 
陈梅香 莆田学院数学与金融学院福建 莆田 351100 
陈智雄 莆田学院数学与金融学院福建 莆田 351100 
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中文摘要:
      针对文献[5]在和与积相等的正定矩阵对的Kantorovich型矩阵不等式证明中所使用的等式是不成立的情况,提出沟通Hermitian矩阵的特征值与惯性关系的方法,得到了和与积相等的Hermitian矩阵对的惯性一般表达式. 不仅证明了文献[5]的矩阵不等式是正确的,而且给出使这类正定(或半正定)矩阵对的通常乘积更精细的矩阵不等式.
英文摘要:
      As the equality used in the proof of Kantorovich’ inequality in for positive definite Hermitian matrix pairs,whose sum is equal to its product,is defective,this paper mediates the relationship between eigenvalue and inertia of Hermitian matrix,and gives us the general expression for Inertia of Hermitian matrix pairs,whose sum is equal to its product. By applications,it not only proves that Kantorovich’ inequality is correct,but also shows some more precise matrix inequalities for product of this class of positive definite (semi-definite) Hermitian matrix pairs.
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