Copyright © 2009 Yongxin Yuan. 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.

Abstract

The inverse eigenvalue problem of constructing symmetric positive semidefinite matrix D (written as D≥0) and real-valued skew-symmetric matrix G (i.e., GT=−G) of order n for the quadratic pencil Q(λ):=λ2Ma+λ(D+G)+Ka, where Ma>0, Ka≥0 are given analytical mass and stiffness matrices, so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors, is considered. Necessary and sufficient conditions under which this quadratic inverse eigenvalue problem is solvable are specified.