Companion matrices and their relations to Toeplitz and Hankel matrices

被引：1

作者：

Luo, Yousong ^{[1
]}

Hill, Robin ^{[2
]}

机构：

[1] RMIT Univ, Sch Math & Geospatial Sci, GPO Box 2476V, Melbourne, Vic 3001, Australia

[2] Univ Melbourne, Dept Elect & Elect Engn, Melbourne, Vic 3010, Australia

来源：

SPECIAL MATRICES | 2015年 / 3卷 / 01期

关键词：

Companion matrix; Toeplitz matrix; Hankel matrix; Bezoutian;

D O I：

10.1515/spma-2015-0021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we describe some properties of companion matrices and demonstrate some special patterns that arise when a Toeplitz or a Hankel matrix is multiplied by a related companion matrix. We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.

引用

页码：214 / 226

页数：13

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