TY - JOUR

T1 - Numerical ranges of row stochastic matrices

AU - Gau, Hwa Long

AU - Wang, Kuo-Zhong

AU - Wu, Pei Yuan

PY - 2016/10/1

Y1 - 2016/10/1

N2 - In this paper, we consider properties of the numerical range of an n-by-n row stochastic matrix A. It is shown that the numerical radius of A satisfies 1≤w(A)≤(1+n)/2, and, moreover, w(A)=1 (resp., w(A)=(1+n)/2) if and only if A is doubly stochastic (resp.,A=[01⋯10]jth for some j, 1≤j≤n). A complete characterization of the A's for which the zero matrix of size n-1 can be dilated to A is also given. Finally, for each n≥2, we determine the smallest rectangular region in the complex plane whose sides are parallel to the x- and y-axis and which contains the numerical ranges of all n-by-n row stochastic matrices.

AB - In this paper, we consider properties of the numerical range of an n-by-n row stochastic matrix A. It is shown that the numerical radius of A satisfies 1≤w(A)≤(1+n)/2, and, moreover, w(A)=1 (resp., w(A)=(1+n)/2) if and only if A is doubly stochastic (resp.,A=[01⋯10]jth for some j, 1≤j≤n). A complete characterization of the A's for which the zero matrix of size n-1 can be dilated to A is also given. Finally, for each n≥2, we determine the smallest rectangular region in the complex plane whose sides are parallel to the x- and y-axis and which contains the numerical ranges of all n-by-n row stochastic matrices.

KW - 15B51

KW - MSC 15A60

UR - http://www.scopus.com/inward/record.url?scp=84974707581&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2016.06.010

DO - 10.1016/j.laa.2016.06.010

M3 - Article

AN - SCOPUS:84974707581

VL - 506

SP - 478

EP - 505

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -