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    題名: A note on extreme correlation matrices
    作者: Li, Chi-kwong;譚必信;Tam, Bit-shun
    貢獻者: 淡江大學數學學系
    關鍵詞: correlation matrix;extreme point;perturbation;rank;linear span
    日期: 1994-07
    上傳時間: 2010-01-28 07:35:42 (UTC+8)
    出版者: Society for Industrial and Applied Mathematics (SIAM)
    摘要: An $n \times n$ complex Hermitian or real symmetric matrix is a correlation matrix if it is positive semidefinite and all its diagonal entries equal one. The collection of all $n \times n$ correlation matrices forms a compact convex set. The extreme points of this convex set are called extreme correlation matrices. In this note, elementary techniques are used to obtain a characterization of extreme correlation matrices and a canonical form for correlation matrices. Using these results, the authors deduce most of the existing results on this topic, simplify a construction of extreme correlation matrices proposed by Grone, Pierce, and Watkins, and derive an efficient algorithm for checking extreme correlation matrices.
    關聯: Siam Journal on Matrix Analysis and Applications 15(3), pp.903-908
    DOI: 10.1137/S0895479892240683
    顯示於類別:[數學學系暨研究所] 期刊論文


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