Angles, triangle inequalities, correlation matrices and metric-preserving and subadditive functions

TL;DR

This paper investigates various triangle inequalities related to angles and correlation matrices, extending the discussion to metric-preserving and subadditive functions, providing new inequalities and insights into matrix positivity.

Contribution

It introduces new inequalities for angles and correlation matrices and extends the analysis to metric-preserving and subadditive functions, broadening the understanding of these mathematical structures.

Findings

Derived new triangle inequalities for angles.

Established inequalities for correlation matrix entries.

Extended results to metric-preserving and subadditive functions.

Abstract

We study the triangle inequalities for angles (with different definitions) and present inequalities concerning the entries of correlation matrices through the positivity of $3\times 3$ matrices. We extend our discussions to the inequalities concerning the triangle triplets with metric-preserving and subadditive functions.