The matrix arithmetic–geometric mean inequality revisited
Copyright policy )The matrix arithmetic–geometric mean inequality revisited
The authors survey the developments of a matrix version of the arithmetic-geometric mean inequality, and discuss other closely related matters. The article can also serve as introduction to the basic ideas and typical problems of the flourishing subject of matrix inequalities. The main sections are: Levels of matrix inequalities, The arithmetic-geometric mean inequalities, Stronger level 2 inequalities, Another level of matrix inequalities, and Other version of the arithmetic-geometric mean inequality.
- University of Jordan Jordan
- Indian Statistical Institute India
Numerical Analysis, Algebra and Number Theory, singular values, matrix inequalities, Pinching, Matrix monotone functions, Inequalities involving eigenvalues and eigenvectors, pinching, unitarily invariant norms, matrix monotone functions, Miscellaneous inequalities involving matrices, Singular values, Unitarily invariant norms, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, Geometry and Topology, Matrix inequalities, arithmetic-geometric mean inequality
Numerical Analysis, Algebra and Number Theory, singular values, matrix inequalities, Pinching, Matrix monotone functions, Inequalities involving eigenvalues and eigenvectors, pinching, unitarily invariant norms, matrix monotone functions, Miscellaneous inequalities involving matrices, Singular values, Unitarily invariant norms, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, Geometry and Topology, Matrix inequalities, arithmetic-geometric mean inequality
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