| Matrix inequality is a very important research field in matrix theory,and has been highly concerned by scholars at home and abroad.In recent decades,matrix inequality has been widely used in quantum mechanics,cybernetics,biomathematics and other fields.But with the development of science and technology,the existing matrix inequality theory can not meet the needs of the development of various industries.Therefore,it is necessary to further study matrix inequality.This thesis mainly studies several kinds of matrix inequalities.This article is divided into four chapters.In chapter 1,we introduce the research background and development process of matrix inequalities,mean inequalities and Heinz inequalities in recent years.In chapter 2,we obtain several refinements matrix mean inequalities by the results of matrix inequalities and the convexity of function.In chapter 3,we mainly study matrix Heinz inequalities,generalize and improve the existing results by using the convexity of function.In chapter 4,we summarize improvement methods of some matrix inequalities and make some prospects of the future work. |
