DocumentCode :
2832489
Title :
The Elliptic Numerical Ranges of 4x4 Matrices
Author :
Liu, Xueting ; Li, Hongkui
Author_Institution :
Sch. of Electr. & Electron. Eng., Shandong Univ. of Technol., Zibo, China
fYear :
2009
fDate :
11-12 July 2009
Firstpage :
566
Lastpage :
569
Abstract :
Suppose be an n-order complex polynomial f(z) = zn + a1zn-1 +ldrldrldr+ an-1z + an. Let be an complex matrix associated with f(z). The numerical range of A is denoted by W(A) = {x* Ax : x isin Cn iota|x| = 1}. In this paper, we consider the properties of the Kippenhahn curve CR (A) firstly, and then discuss the necessary condition of W (A) being an elliptic disc by making use of matrices Kronecker product and the Kippenhahn curve CR (A) when A is 4 times 4 reducible companion matrix.
Keywords :
polynomial matrices; Kippenhahn curve; complex matrix; elliptic disc; elliptic numerical ranges; n-order complex polynomial; reducible companion matrix; Automatic control; Automation; Chromium; Control systems; Educational institutions; Eigenvalues and eigenfunctions; Linear matrix inequalities; Polynomials; Shape; Systems engineering and theory; Companion matrix; Kronecker product; Numerical range; elliptic disc;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Control, Automation and Systems Engineering, 2009. CASE 2009. IITA International Conference on
Conference_Location :
Zhangjiajie
Print_ISBN :
978-0-7695-3728-3
Type :
conf
DOI :
10.1109/CASE.2009.151
Filename :
5194517
Link To Document :
https://search.ricest.ac.ir/dl/search/defaultta.aspx?DTC=49&DC=2832489
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