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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 016 185 05X  
Author(s):  
Li, ChiKwong; mathias, Roy:  
Shorttitle:  
Construction of matrices with prescribed singular values and eigenvalues  
Source:  
BIT 41, No. 1, 115  126 (2001).  
Classification:  
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
eigenvalues and singular values; mutual compatibility (majorization) conditions; reconstruction of matrices; reconstruction of real matrices;  
Review:  
The necessary and sufficient condition of existence of a complex square matrix with prescribed (nonnegative) singular values and (complex) eigenvalues (viz., the Weyl  Horn inequalities) is generalized to the case where not all the eigenvalues are prescribed (and, by the way, an amusing observation about the ``missing" eigenvalues is made in this context) and then, the construction itself is addressed. The current available algorithms are made more sophisticated  the order of eigenvalues may be prescribed in triangular case. This idea improves the recent Chu's algorithm and, as the most important consequence, the matrix may be required real (one first constructs its blocktriangular predecessor with the necessary twobytwo partitioning).  
Remarks to the editors:  