摘要
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.
原文 | ???core.languages.en_GB??? |
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頁(從 - 到) | 478-505 |
頁數 | 28 |
期刊 | Linear Algebra and Its Applications |
卷 | 506 |
DOIs | |
出版狀態 | 已出版 - 1 10月 2016 |