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Journal of Applied Mathematics
Volume 2014, Article ID 703178, 9 pages
Research Article

Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems

Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 2 September 2013; Accepted 15 December 2013; Published 21 January 2014

Academic Editor: Zhongxiao Jia

Copyright © 2014 Hong-Xiu Zhong et al. 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.


Given pairs of complex numbers and vectors (closed under conjugation), we consider the inverse quadratic eigenvalue problem of constructing real matrices , , , and , where , and are symmetric, and is skew-symmetric, so that the quadratic pencil has the given pairs as eigenpairs. First, we construct a general solution to this problem with . Then, with the special properties and , we construct a particular solution. Numerical results illustrate these solutions.