SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 478-503, March 2024.
Abstract. We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column) completion problem of a polynomial matrix of given degree under different prescribed invariants: the whole eigenstructure, all of it but the row (column) minimal indices, and the finite and/or infinite structures. Moreover, we characterize the existence of a polynomial matrix with prescribed degree and eigenstructure over an arbitrary field.

中文翻译：

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给定次数多项式矩阵的行或列完成

《SIAM 矩阵分析与应用杂志》，第 45 卷，第 1 期，第 478-503 页，2024 年 3 月。
摘要。我们解决了当规定了特征结构（或部分）和某些行（列）时表征固定次数多项式矩阵的存在性的问题。更具体地说，我们提出了在不同规定不变量下给定次数多项式矩阵的行（列）完成问题的解决方案：整个特征结构，除了行（列）最小索引之外的所有特征，以及有限和/或无限结构。此外，我们还描述了在任意域上具有规定次数和特征结构的多项式矩阵的存在性。