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Name:
Miloslav Znojil
Reviewer number:
9689
Email:
znojil@ujf.cas.cz
Item's zbl-Number:
DE 016 185 05X
Author(s):
Li, Chi-Kwong; mathias, Roy:
Shorttitle:
Construction of matrices with prescribed singular values and eigenvalues
Source:
BIT 41, No. 1, 115 - 126 (2001).
Classification:
Primary Classification:
15A18Eigenvalues, singular values, and eigenvectors
Secondary Classification:
15A42Inequalities involving eigenvalues and eigenvectors
65F18Inverse eigenvalue problems
15A29Inverse problems
Keywords:
eigenvalues and singular values; mutual compatibility (majorization) conditions; re-construction of matrices; re-construction 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 block-triangular
predecessor with the necessary two-by-two partitioning).


Remarks to the editors:

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