THE NUMERICAL RANGE OF MATRIX PRODUCTS

被引：0
|
作者：
Drury, Stephen [1 ]
机构：
[1] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 0B9, Canada
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2024年 / 40卷
关键词：
Numerical range; Matrix product;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss what can be said about the numerical range of the matrix product A(1 )A(2) when the numerical ranges of A(1 )and A(2) are known. If two compact convex subsets K-1, K-2 of the complex plane are given, we discuss the issue of finding a compact convex subset K such that whenever A(j) (j = 1,2) are either unrestricted matrices or normal matrices of the same shape with W(A(j)) subset of K-j, it follows that W(A(1) A(2)) subset of K. We do this by defining specific deviation quantities for both the unrestricted case and the normal case.
引用
收藏
页码：307 / 321
页数：15
相关论文
共 50 条
  • [1] Preservers of numerical range of matrix skew products
    Bendaoud, M.
    Benyouness, A.
    Sarih, M.
    ACTA SCIENTIARUM MATHEMATICARUM, 2024,
  • [2] On the numerical range of a matrix
    Zachlin, Paul F.
    Hochstenbach, Michiel E.
    LINEAR & MULTILINEAR ALGEBRA, 2008, 56 (1-2): : 185 - 225
  • [3] On the Determinantal Range of Matrix Products
    Guterman A.
    Soares G.
    Journal of Mathematical Sciences, 2018, 232 (6) : 805 - 815
  • [4] The upper numerical range of a quaternionic matrix is not a complex numerical range
    Thompson, RC
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 254 : 19 - 28
  • [5] Numerical range of a continuant matrix
    Chien, MT
    Huang, JM
    APPLIED MATHEMATICS LETTERS, 2001, 14 (02) : 213 - 216
  • [6] On the boundary of the numerical range of a matrix
    Chien, Mao-Ting
    Yeh, Lina
    APPLIED MATHEMATICS LETTERS, 2010, 23 (06) : 725 - 727
  • [7] A GENERALIZATION OF THE NUMERICAL RANGE OF A MATRIX
    LENFERINK, HWJ
    SPIJKER, MN
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 140 : 251 - 266
  • [8] NUMERICAL RANGE OF MATRIX POLYNOMIALS
    LI, CK
    RODMAN, L
    SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1994, 15 (04) : 1256 - 1265
  • [9] The numerical range of a nonnegative matrix
    Li, CW
    Tam, BS
    Wu, PY
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 350 : 1 - 23
  • [10] On the numerical ranges of matrix products
    Chien, Mao-Ting
    Ko, Chung-Lien
    Nakazato, Hiroshi
    APPLIED MATHEMATICS LETTERS, 2010, 23 (06) : 732 - 737
12345