福州大学学报（自然科学版）2018，Vol.46Issue(1)：27-31,5.DOI:10.7631/issn.1000-2243.16378
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
摘要
Abstract
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.关键词
Hermitian矩阵/惯性/矩阵方程/秩Key words
Hermitian matrix/inertia/matrix equation/rank of matrix分类
数理科学引用本文复制引用
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):27-31,5.基金项目
国家自然科学基金资助项目(61373140) （61373140）
福建省自然科学基金资助项目(2017J01565) （2017J01565）
福建省高校杰出青年科研人才培育计划(2016) （2016）
福建省教育厅中青年教师教育科研资助项目(JAT170499) （JAT170499）
莆田学院教改资助项目(JG201630) （JG201630）
莆田学院育苗基金资助项目(2016110) （2016110）
