Matrix Reconstruction with Prescribed Diagonal Elements, Eigenvalues, and Singular Values
نویسندگان
چکیده
DIAGONAL ELEMENTS, EIGENVALUES, AND SINGULAR VALUES DRAFT AS OF April 30, 2013 SHENG-JHIH WU AND MOODY T. CHU Abstract. Diagonal entries and eigenvalues of a Hermitian matrix, diagonal entries and singular values of a general matrix, and eigenvalues and singular values of a general matrix satisfy necessarily some majorization relationships which turn out also to be sufficient conditions. The inverse problem of numerically reconstructing a matrix to satisfy any given set of data meeting one of these relationships has been solved. In this paper, we take one step further to construct a matrix satisfying prescribed diagonal elements, eigenvalues, and singular values simultaneously. Theory of the existence of such a matrix is established and a numerical method is proposed.
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