Study Of Schur Complement And Fischer Inequality

Matrix inequalities have important application in studying of matrix theory, and Schur complement of matrix and Fischer inequality problem are hot topics of researching on matrix inequalities.For the past few years,many scholars have done a lot of researches in both areas.Against these two types of problems,They can not only deal with large-scale matrix calculation,but also have certain application value in linear programming.So these two kinds of problems of Schur complement and Fischer inequality are worthy studying.This paper will discuss from the following two aspects.On the one hand,This paper mainly researches equations and inequalities problems of Schur complement.Introduces some matrix equations of Schur complement through these methods of analogy、structure and transform according to the definition of Schur complement on the basis of the existing literature,and derives some matrix inequalities, their deformations and some related special operations from these matrix equations.On the other hand, This paper mainly researches application of Fischer inequality, n ?n matrix, m ?n matrix and associated with tensile matrix are applied to partitioned matrix,and derives some new results through these methods of structure and transform on the basis of researching Fischer inequality.