TY - JOUR

T1 - Numerical range of a normal compression II

AU - Gau, Hwa Long

AU - Wu, Pei Yuan

N1 - Funding Information:
Research supported by the National Science Council of the Republic China. ∗ Corresponding author. E-mail addresses: [email protected] (H.-L. Gau), [email protected] (P.Y. Wu).

PY - 2004/10/1

Y1 - 2004/10/1

N2 - As in the predecessor [Numerical range of a normal compression, Linear and Multilinear Algebra, in press] of this paper, we consider properties of matrices of the form V*NV, where N=diag(a1,⋯,a n+1) is a diagonal matrix with distinct eigenvalues ajs such that each of them is a corner of the convex hull they generate, and V is an (n+1)-by-n matrix with V*V=In such that any nonzero vector orthogonal to the range space of V has all its components nonzero. We obtain that such a matrix A is determined by its eigenvalues up to unitary equivalence, is irreducible and cyclic, and the boundary of its numerical range is a differentiable curve which contains no line segment. We also consider the condition for the existence of another matrix of the above type which dilates to A such that their numerical ranges share some common points with the boundary of the (n+1)-gon a1⋯an+1.

AB - As in the predecessor [Numerical range of a normal compression, Linear and Multilinear Algebra, in press] of this paper, we consider properties of matrices of the form V*NV, where N=diag(a1,⋯,a n+1) is a diagonal matrix with distinct eigenvalues ajs such that each of them is a corner of the convex hull they generate, and V is an (n+1)-by-n matrix with V*V=In such that any nonzero vector orthogonal to the range space of V has all its components nonzero. We obtain that such a matrix A is determined by its eigenvalues up to unitary equivalence, is irreducible and cyclic, and the boundary of its numerical range is a differentiable curve which contains no line segment. We also consider the condition for the existence of another matrix of the above type which dilates to A such that their numerical ranges share some common points with the boundary of the (n+1)-gon a1⋯an+1.

KW - Cyclic matrix

KW - Irreducible matrix

KW - Normal compression

KW - Numerical range

UR - http://www.scopus.com/inward/record.url?scp=4344612910&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2004.04.013

DO - 10.1016/j.laa.2004.04.013

M3 - 期刊論文

AN - SCOPUS:4344612910

SN - 0024-3795

VL - 390

SP - 121

EP - 136

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -