论文标题
伴侣单位下赫森伯格矩阵
Companion unit lower Hessenberg matrices
论文作者
论文摘要
近年来，人们对伴侣矩阵的兴趣越来越大。人们对稀疏伴侣矩阵有深入的了解，特别是知道，每个稀疏的伴随矩阵都可以通过任何组合，置换相似性和对角线相似性转换为一个特别简单的赫森伯格矩阵。后者对于非SPARSE的伴侣矩阵并不正确，尽管众所周知，每个非SPARSE伴随矩阵都是非构造的。在这项工作中，将描述单位较低的赫森伯格的非Sparse伴侣矩阵。还考虑了自然概括。
In recent years there has been a growing interest in companion matrices. There is a deep knowledge of sparse companion matrices, in particular it is known that every sparse companion matrix can be transformed into a unit lower Hessenberg matrix of a particularly simple type by any combination of transposition, permutation similarity and diagonal similarity. The latter is not true for the companion matrices that are non-sparse, although it is known that every non-sparse companion matrix is nonderogatory. In this work the non-sparse companion matrices that are unit lower Hessenberg will be described. A natural generalization is also considered.
