As a special topic in matrix analysis, majorization is an important tool in deriving inequalities of eigenvalues, singular values, and norms of matrices. It has a wide range of application in other fields such as optimization, statistics, etc. We introduce the concept of majorization, present its basic properties, and show some matrix inequalities in majorization.

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Majorization and Matrix Inequalities

  • Fuzhen Zhang

摘要

As a special topic in matrix analysis, majorization is an important tool in deriving inequalities of eigenvalues, singular values, and norms of matrices. It has a wide range of application in other fields such as optimization, statistics, etc. We introduce the concept of majorization, present its basic properties, and show some matrix inequalities in majorization.