Trimmed linearizations for structured matrix polynomials (Q952032)

The authors discuss the eigenvalue problem for general and structured matrix polynomials that may be singular and may have eigenvalues at infinity. Condensed forms that allow deflation of the infinite eigenvalue and a singular structure of the matrix polynomial are derived. The remaining reduced order canonical form leads to a new types of linearizations that determine the finite eigenvalues and corresponding eigenvectors. It is shown that the new linearizations also simplify the construction of structure preserving linearizations.