A refined determinantal inequality for correlation matrices
Niushan Gao, Alexandra Kirillova, Zihao Tong
TL;DR
This paper improves upon Olkin's upper bound for the determinant of correlation matrices by extending and refining the original inequality, providing a tighter mathematical bound.
Contribution
It introduces a new, more accurate inequality for the determinants of correlation matrices, advancing theoretical understanding in matrix analysis.
Findings
Derived a refined upper bound for correlation matrix determinants
Extended Olkin's original inequality with a tighter bound
Contributed to the mathematical theory of correlation matrices
Abstract
Olkin [3] obtained a neat upper bound for the determinant of a correlation matrix. In this note, we present an extension and improvement of his result.
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Taxonomy
TopicsMathematical Inequalities and Applications · Matrix Theory and Algorithms · Advanced Mathematical Theories and Applications