On the Inverse Symmetric Quadratic Eigenvalue Problem

  title={On the Inverse Symmetric Quadratic Eigenvalue Problem},
  author={Peter Lancaster and Ion Zaballa},
  journal={SIAM J. Matrix Anal. Appl.},
The detailed spectral structure of symmetric, algebraic, quadratic eigenvalue problems has been developed recently. In this paper we take advantage of these canonical forms to provide a detailed analysis of inverse problems of the following form: construct the coefficient matrices from the spectral data including the classical eigenvalue/eigenvector data and sign characteristics for the real eigenvalues. An orthogonality condition dependent on these signs plays a vital role in this construction… 
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