The generic change of the Weierstraß canonical form of regular complex structured matrix pencils under generic structure-preserving additive low-rank perturbations is studied. Several different symmetry structures are considered, and it is shown that for most of the structures, the generic change in the eigenvalues is analogous to the case of generic perturbations that ignore the structure. However, for some odd/even and palindromic structures, there is a different behavior for the eigenvalues 0 and \(\infty \), respectively, \(+1\) and \(-1\). The differences arise in those cases where the parity of the partial multiplicities in the perturbed matrix pencil provided by the generic behavior in the general structure-ignoring case is not in accordance with the restrictions imposed by the structure. The new results extend results for the rank-1 and rank-2 cases that were obtained in Batzke (Linear Algebra Appl 458:638–670, 2014, Oper Matrices 10:83–112, 2016) for the case of special structure-preserving perturbations. As the main tool, we use decompositions of matrix pencils with symmetry structure into sums of rank-1 matrix pencils, as those allow a parametrization of the set of matrix pencils with a given symmetry structure and a given rank.

研究了在保持通用结构的加性低秩扰动下，普通复杂结构矩阵铅笔的Weierstraß规范形式的通用变化。考虑了几种不同的对称结构，并且表明对于大多数结构，特征值的一般性变化类似于忽略结构的一般性扰动的情况。但是，对于某些奇/偶和回文结构，特征值0和\（\ infty \）分别具有\（+ 1 \）和\（-1 \）具有不同的行为。。在忽略普通结构的情况下，由通用行为提供的扰动矩阵笔中的部分多重奇偶校验的奇偶校验与结构所施加的约束不一致时，会产生差异。对于保留特殊结构的情况，新结果扩展了在Batzke中获得的1级和2级案例的结果（Linear Algebra Appl 458：638–670，2014； Oper Matrices 10：83–112，2016）。扰动。作为主要工具，我们将具有对称结构的矩阵铅笔分解为等级为1的矩阵铅笔的总和，因为这些分解允许对具有给定对称结构和给定等级的矩阵铅笔集合进行参数化。