Eventually Nekrasov Matrices And Eventually Generalized DZ Matrices

The judgment of nonsingularity of matrices,the infinity norm bounds of the inverse of nonsingular matrices,and the eigenvalue localization of matrices play important roles in many fields of linear algebra and its applications.This paper studies these three problems,introduces two new classes of nonsingular matrices:Eventually Nekrasov matrices and Eventually generalized DZ matrices,and studies the infinity norm bounds of the inverse of the two kinds of matrices and the eigenvalue localization of matrices.The main contents are as follows:In Chapter 1:The background and significance of the topic,the research status at home and abroad are briefly introduced,and the concepts,definitions,lemmas and theorems needed in this paper are listedIn Chapter 2:A new class of nonsingular matrices:Eventually Nekrasov matrices is introduced.By using the existing upper bounds of the infinite norm of the inverse of Nekrasov matrices,the upper bounds of the infinite norm of the inverse of Eventually Nekrasov matrices are givenIn Chapter 3:Firstly,the upper bounds of the infinite norm of the inverse of Even-tually DZ matrix are given by using the existing upper bounds of the infinite norm of the inverse of DZ matrices.Secondly,a new class of nonsingular matrices named Generalized DZ matrices is introduced.A new eigenvalue localization theorem is given by constructing the exclusion sets of eigenvalues of matrices,which is used to prove that Generalized DZ matrices are nonsingular matrices.Finally,another class of nonsingular matrices named Eventually generalized DZ matrices is introduced.An eigenvalue localization theorem with two parameters is given based on the nonsingu-larity of Eventually generalized DZ matricesIn Chapter 4:The works done in this paper are summarized and the future re-search problems are presented.