Point equation of the boundary of the numerical range of a matrix polynomial

被引:14
|
作者
Chien, MT
Nakazato, H
Psarrakos, P
机构
[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece
[2] Soochow Univ, Dept Math, Taipei 11102, Taiwan
[3] Hirosaki Univ, Fac Sci & Technol, Dept Math Syst Sci, Hirosaki, Aomori 0368561, Japan
关键词
matrix polynomial; numerical range; boundary; discriminant;
D O I
10.1016/S0024-3795(01)00549-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The numerical range of an n x n matrix polynomial P(lambda) = A(m)lambda(m) + A(m-1)lambda(m-1) + .... + A(1)lambda + A(0) is defined by W(P) = {lambda is an element of C : x * P (lambda)x = 0, x is an element of C-n, x not equal 0}. For the linear pencil P(lambda) = Ilambda - A, the range W(P) coincides with the numerical range of matrix A, F(A) = {x*Ax: x is an element of C-n, x*x = 1}. In this paper, we obtain necessary conditions for the origin to be a boundary point of F(A). As a consequence, an algebraic curve of degree at most 2n(n - 1)m, which contains the boundary of W(P), is constructed. (C) 2002 Elsevier Science Inc. All rights reserved.
引用
收藏
页码:205 / 217
页数:13
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