TY - GEN A1 - Byers, Ralph A1 - Mehrmann, Volker A1 - Xu, Hongguo T1 - Staircase forms and trimmed linearizations for structured matrix polynomials N2 - We discuss the eigenvalue problem for general and structured matrix polynomials which may be singular and may have eigenvalues at infinity. We derive staircase condensed forms that allow deflation of the infinite eigenvalue and singular structure of the matrix polynomial. The remaining reduced order staircase form leads to new types of linearizations which determine the finite eigenvalues and and corresponding eigenvectors. The new linearizations also simplify the construction of structure preserving linearizations. KW - matrix polynomial KW - singular matrix polynomial KW - Kronecker chain KW - staircase form KW - linearization KW - trimmed linearization KW - structured KW - trimmed linearization Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/394 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3944 ER -