TY - GEN A1 - Batzke, Leonhard A1 - Mehl, Christian T1 - On the inverse eigenvalue problem for $T$-alternating and $T$-palindromic matrix polynomials N2 - The inverse eigenvalue problem for $T$-alternating matrix polynomials over arbitrary algebraically closed fields of characteristic different from two is considered. The main result shows that the necessary conditions obtained in \cite{MacMMM10} for a matrix polynomial to be the Smith form of a $T$-alternating matrix polynomial are under mild conditions also sufficient to be the Smith form of a $T$-alternating matrix polynomial with invertible leading coefficient which is additionally in anti-triangular form.. In particular, this result implies that any $T$-alternating matrix polynomial with invertible leading coefficient is equivalent to a $T$-alternating matrix polynomial in anti-triangular form that has the same finite and infinite elementary divisors as the original matrix polynomial. Finally, the inverse eigenvalue problem for $T$-palindromic matrix polynomials is considered excluding the case that both $+1$ and $-1$ are eigenvalues. KW - matrix polynomial KW - alternating matrix polynomial KW - triangularization KW - palindromic matrix polynomial Y1 - 2013 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1251 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12513 ER -