Optimal quadratic bounds for the largest eigenvalue of correlation matrices under restricted information

Abstract

A previous method used for bounding the largest eigenvalue of a 3x3 correlation matrix is extended to higher dimensions. Optimal quadratic bounds by given determinant and traces of the correlation matrix powers are derived for a class of correlation matrices under specific restricted information. Conditions under which these bounds are more stringent than the bounds by Wolkowicz and Styan (1980) are determined