ویراساینس.
سند علمی

Matrix Inequalities and Partial Isometries that Arise in X-ray Crystallography

Chi-Kwong Li

چکیده

In X-ray crystallography, one needs to consider matrices of the form P = (X T X)=M, where X 2 IR M n has rows X i : with 1 i M such that jX i :vj c and kX i :k = 1 for some given c 2 (0; 1) and v 2 IR n. Using the theory of majorization, we give a short proof for some inequalities relating the eigenvalues of P ?1 when P is invertible. Matrices X that minimize det (P ?1) or tr (P ?1) are constructed. These extend some results of Ortner and Krr auter and connrm their conjecture on the subject.

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