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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.

Optimal Bounds for the Largest Eigenvalue of a 3 &#215; 3 Correlation Matrix

Optimal Bounds for the Largest Eigenvalue of a 3 × 3 Correlation Matrix