• 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.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2832489