Research On Matrix Singular Value Inequalities And Special Matrices

Matrix thematic theory is a hot branch of algebra,matrix has important research value,in recent years,experts and scholars to study it seriously.Related matrix inequality for strengthening and promotion,makes a further development of matrix theory.At present,the development of the matrix theory and quantum theory can be extended to the operator,and makes the effect of matrix wider.Based on the existing matrix singular value inequality and the special nature of the matrix theory,based on the matrix singular value inequality related theories and achievements,formal equivalent characterizations of the matrix,the nature of the normal matrix,obtained the Hermite matrix eigenvalues of optimization problem and use the Courant-Fischer theorem Hermiite matrix eigenvalues inequality,below is the content of chapter four:The first chapter mainly illustrates the article used some of the basic symbols,basic concept and the fundamental lemma.Including singular value of matrix and characteristic value,singular value decomposition,schur decomposition,regular matrix,Hermite matrix and the related theorem.The second chapter first gives several definitions and lemma,using the singular value decomposition of matrix,obtained the singular values and the relationship between characteristic value,obtained the principal diagonal elements of the matrix,the trace,the spectral norm and norm,and the relation of inequality between of matrix singular value.The third chapter mainly for a special kind of matrix normal matrix are studied,equivalent characterizations of normal matrix,obtained the inner product of normal matrices inequalities and norm inequalities.The fourth chapter mainly based on the Hermite matrix of Hermite matrices is given the definition,properties and characteristics related to depict,studies the optimization Hermite matrix eigenvalue problem,using the courant---fischer minimax theorem eigenvalues inequality for the promotion.