SHARP LOWER BOUNDS FOR THE DIMENSION OF LINEARIZATIONS OF MATRIX POLYNOMIALS

被引：15
作者：
De Teran, Fernando [1 ]
Dopico, Froilan M. [2 ,3 ]
机构：
[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
[2] Univ Carlos III Madrid, CSIC, UAM UCM UC3M, Inst Ciencias Matemat, Leganes 28911, Spain
[3] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2008年 / 17卷
关键词：
Matrix polynomials; Matrix pencils; Linearizations; Dimension;
D O I：
10.13001/1081-3810.1281
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A standard way of dealing with matrix polynomial eigenvalue problems is to use linearizations. Byers, Mehrmann and Xu have recently defined and studied linearizations of dimensions smaller than the classical ones. In this paper, lower bounds are provided for the dimensions of linearizations and strong linearizations of a given m x n matrix polynomial, and particular linearizations are constructed for which these bounds are attained. It is also proven that strong linearizations of an n x n regular matrix polynomial of degree l must have dimension nl x nl.
引用
收藏
页码：518 / 531
页数：14
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