Polynomial numerical hulls of matrix polynomials

被引：7
|
作者：
Salemi, A. [1 ]
Aghamollaei, Gh. R.
机构：
[1] Shahid Bahonar Univ Kerman, Dept Math, Kerman 7619614111, Iran
[2] Islamic Azad Univ Kerman, Dept Math, Kerman, Iran
来源：
LINEAR & MULTILINEAR ALGEBRA | 2007年 / 55卷 / 03期
关键词：
polynomial numerical hull; matrix polynomial; joint polynomial numerical hull;
D O I：
10.1080/03081080500431497
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M(n) be the algebra of all n x n complex matrices. Suppose Q(lambda) = A(m)lambda(m) + A(m-1)lambda(m-1) + center dot center dot center dot + A(1)lambda + A(0) is a matrix polynomial, where A(i) is an element of M(n) (i = 0, 1,..., m) and lambda is a complex variable. In this note, we introduce the polynomial numerical hull and the joint polynomial numerical hull of order k of Q(lambda). The emphasis is on the geometric properties of polynomial numerical hulls of matrix polynomials. Also, we study the relationships among spectra, numerical ranges and polynomial numerical hulls of order k of matrix polynomials.
引用
收藏
页码：219 / 228
页数：10
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