TITLE:
Optimal Bounds for the Largest Eigenvalue of a 3 × 3 Correlation Matrix
AUTHORS:
Werner Hürlimann
KEYWORDS:
Correlation Matrix, Positive Semi-Definite Matrix, Extreme Point, Eigenvalue, Inequality
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.7,
June
2,
2015
ABSTRACT: A new approach that bounds the largest eigenvalue of 3 × 3 correlation
matrices is presented. Optimal bounds by given determinant and trace of the
squared correlation matrix are derived and shown to be more stringent than the
optimal bounds by Wolkowicz and Styan in specific cases.