Study On The Inequalities Of Positive Definite Matrices And The Numerical Characteristics Of Matrices

As an important tool to study mathematics and its applications, matrix has a widerange of applications in mathematics disciplines and many other scientific fields. Thepurpose of this thesis is to discuss the inequalities of the positive definite matrices andthe numerical characteristics of matrices. The main results and innovations are asfollows:1. By applying the properties of positive matrix and linear algebra theories, somematrix version inequalities of some classic Characteristics inequalities are obtained.There are the improvements of the earlier results.2. Based on the estimation of the eigenvalues and inequality theories, a newestimate of matrix’s spread is present, the inequality is given as followsBased on the conclusions, a nonsingular principle is obtained.3. One good result of the estimation of matrix’s determinant is given as followsThe conclusion is better than the Hadamard inequality.4. In order to increase the preciseness, the effectiveness and superiority of theresults are demonstrated in the thesis, and some numerical examples are cited.