Symmetric Means and Matrix Inequalities

Inequalities for symmetric means

We study Muirhead-type generalizations of families of inequalities due to Newton, Maclaurin and others. Each family is defined in terms of a commonly used basis of the ring of symmetric functions in n variables. Inequalities corresponding to elementary symmetric functions and power sum symmetric functions are characterized by the same simple poset which generalizes the majorization order. Some ...

Power matrix means and related inequalities ∗

This survey paper contains recent results for power matrix means and related inequalities for convex functions, Hadamard product of matrices as well as some inequalities involving exponential function of matrices.

Matrix inequalities by means of embedding

In this expository study some basic matrix inequalities obtained by embedding bilinear forms 〈Ax, x〉 and 〈Ax, y〉 into 2 × 2 matrices are investigated. Many classical inequalities are reproved or refined by the proposed unified approach. Some inequalities involving the matrix absolute value |A| are given. A new proof of Ky Fan’s singular value majorization theorem is presented.

Ela Matrix Inequalities by Means of Embedding

In this expository study some basic matrix inequalities obtained by embedding bilinear forms 〈Ax, x〉 and 〈Ax, y〉 into 2 × 2 matrices are investigated. Many classical inequalities are reproved or refined by the proposed unified approach. Some inequalities involving the matrix absolute value |A| are given. A new proof of Ky Fan’s singular value majorization theorem is presented.

RANDOM WALKS ON SYMMETRIC SPACESAND INEQUALITIES FOR MATRIX SPECTRAAlexander