Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 513582, 25 pages
Research Article

Explicit Solution of the Inverse Eigenvalue Problem of Real Symmetric Matrices and Its Application to Electrical Network Synthesis

D. B. Kandić1 and B. D. Reljin2

1Department of Physics & Electrical Engineering, Mechanical Engineering Faculty, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
2Electrical Engineering Faculty, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia

Received 20 January 2008; Accepted 22 May 2008

Academic Editor: Mohammad Younis

Copyright © 2008 D. B. Kandić and B. D. Reljin. 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.


A novel procedure for explicit construction of the entries of real symmetric matrices with assigned spectrum and the entries of the corresponding orthogonal modal matrices is presented. The inverse eigenvalue problem of symmetric matrices with some specific sign patterns (including hyperdominant one) is explicitly solved too. It has been shown to arise thereof a possibility of straightforward solving the inverse eigenvalue problem of symmetric hyperdominant matrices with assigned nonnegative spectrum. The results obtained are applied thereafter in synthesis of driving-point immittance functions of transformerless, common-ground, two-element-kind RLC networks and in generation of their equivalent realizations.