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.
"Solutions of a Quadratic Inverse Eigenvalue Problem for Damped Gyroscopic Second-Order Systems." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/703178