SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1510-1539, December 2023.
Abstract. The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank-one perturbations.

中文翻译：

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关于矩阵铅笔的特征不变量和线性关系

《SIAM 矩阵分析与应用杂志》，第 44 卷，第 4 期，第 1510-1539 页，2023 年 12 月。
摘要。研究了线性关系和矩阵铅笔之间的关系。给定线性关系，我们引入其 Weyr 特性。如果线性关系是给定矩阵铅笔的范围（或核）表示，我们表明该特征与铅笔的克罗内克规范形式之间存在对应关系。利用这种关系来获得对矩阵笔在一级扰动下的不变特性的估计。