Convex maps on R^n and positive definite matrices

TL;DR

This paper explores convex functions related to positive definite matrices on R^n, leading to new and unusual Holder matrix inequalities that expand the understanding of matrix analysis.

Contribution

It introduces novel convex functions on R^n connected to positive definite matrices, resulting in exotic Holder matrix inequalities.

Findings

Development of new convex functions associated with positive definite matrices

Derivation of exotic Holder matrix inequalities

Enhanced understanding of matrix inequalities in convex analysis

Abstract

We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.