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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 018 027 917  
Author(s):  
Xie, Dongxiu; Hu, Xiyan; Zhang, Lei:  
Shorttitle:  
The solvability conditions for inverse eigenvalue problem of antibisymmetric matrices.  
Source:  
J. Comput. Math. 20, No. 3, 245  256 (2002).  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
Inverse eigenvalue problem; Frobenius norm; approximate solution by a real biantisymmetric matrix  
Review:  
Among all the inverse eigenvalue problems the authors pick up the following two. Problem I: Given X (= m complex eigenvectors of some A) and knowing the m related complex eigenvalues, search for A in the class of the so called antibisymmetric n by n real matrices (i.e., matrices which are antisymmetric with respect to both main diagonals). Problem II: Over the solution set, find an element with the minimal distance (in the sense of Frobenius norm) from a given real matrix. In the second context, the authors construct the solution set and give the expression for the solution, separating the even and odd dimensions n. In the former problem, they also add some necessary and sufficient conditions of its solvability.  
Remarks to the editors:  