Matrix Singular Value Inequalities And Similarity Studies

Matrix theory is an important branch of algebra and has a good research significance.It could help to solve some complex problems and have advantages of statement concise and study thoroughly.So it becomes a major tool in dealing with mathematics and other disciplines.Singular value inequality application palys a significant role in the calculation.For years,some experts research on the problems about singular value by using different ways,and make this system has a great development.Based on the existing theorem,this article gets a series of singular value inequality and some properties about matrix absolute value and replacement of inequality by making use of sequencing inequality,properties about permutation matrix and matrix absolute value,Takagi theorem,some inequalities ahout consimilarity and unitary similar.This article is divided into four chapters,specific content of each chapter are as follows:The first chapter emphasize some simple symbols,basic concepts and theories referred in this article.The doubly stochastic matrices,nonnegative matrices, permutation matrix,singular value decomposition,weak majorization,and other related theorems are included in this chapter.The second chapter firstly give some correlation theorem of singular value inequalities,then we give some results about singular value inequalities.The third chapter gets some inequalities about weak majorization and matrix norm by using some theorems weak majorization,some properties about matrix norm and permutation matrix and matrix absolute value.The fourth chapter makes use of some theorems about trangulation and unitary, introduces the conditions of matrix trangulation joint diagonalization, trangulation and unitary, unitary joint diagonalization. Then we present some results about this aspect.