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

2014/07/10 by Diego J. Castaño, Castano, Diego, Vehbi Emrah Paksoy +3
Computer Science · Mathematics · #15A03 #15A45 #39B62 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematics and Applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1407.2800

openalex publication_date 2014/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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× 3 matrices. We extend our discussions to the inequalities concerning the triangle triplets with metric-preserving and subadditive functions.

Citations

• The Rotation of Eigenvectors by a Perturbation. III

Related

• The Shape of Correlation Matrices
• Matrix subadditivity inequalities and block-matrices
• Quasi-triangle inequality for absolute correlation distance
• Correlation between Angle and Side
• Matrices related to the Pascal triangle