Copyright © 2010 Linlin Zhao and Guoliang Chen. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We first consider the following inverse eigenvalue problem: given and a diagonal matrix , find Hermite-Hamilton matrices and such that . We then consider an optimal approximation problem: given Hermitian matrices and , find a solution of the above inverse problem such that . By using the Moore-Penrose generalized inverse and the singular value decompositions, the solvability conditions and the representations of the general solution for the first problem are derived. The expression of the solution to the second problem is presented.