Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2008, Article ID 513582, 25 pages doi:10.1155/2008/513582 Research Article Explicit Solution of the Inverse Eigenvalue Problem of Real Symmetric Matrices and Its Application to Electrical Network Synthesis D. B. Kandi´ c 1 and B. D. Reljin 2 1 Department of Physics & Electrical Engineering, Mechanical Engineering Faculty, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia 2 Electrical Engineering Faculty, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia Correspondence should be addressed to D. B. Kandi´ c, dbkandic@afrodita.rcub.bg.ac.yu Received 20 January 2008; Accepted 22 May 2008 Recommended by Mohammad Younis 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. Copyright q 2008 D. B. Kandi´ c 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. 1. Introduction During the past few decades,many papers 1–16 have studied the inverse eigenvalue problems IEPs of various types. The solution existence of the specific IEPs was generally considered in 1, 3–8, 10, 11, 13, 14 without explicit formulation of the corresponding procedure for solution construction, whereas in 2, 9, 12, 15, 16 this has been accomplished. The main result of 16 is the proof that IEP of symmetric hyperdominant hd matrices with assigned nonnegative spectrum has at least one solution which has also been constructed. This settled an old IEP opened in 17.Hyperdominant matrices have nonnegative diagonal and nonpositive off-diagonal entries and nonnegative hd margins of rows hd margin of a row is the sum of entries in that row. The tool used in 16 to construct the nth-order hd matrix with assigned spectrum was the nth-order orthogonal Hessenberg matrix constructed as a special product of n - 1 plane rotations 15. Hessenberg matrices naturally arise in study