標題: Numerical ranges as circular discs
作者: Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: Numerical range;Geometric multiplicity;Algebraic multiplicity;Normal matrix
公開日期: 1-十二月-2011
摘要: We prove that if a finite matrix A of the form [(al)(0) (B)(C)]is such that its numerical range W (A) is a circular disc centered at a, then a must be an eigenvalue of C. As consequences, we obtain, for any finite matrix A, that (a) if aW (A) contains a circular arc, then the center of this circle is an eigenvalue ofA with its geometric multiplicity strictly less than its algebraic multiplicity, and (b) if A is similar to a normal matrix, then aW (A) contains no circular arc. (C) 2011 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.aml.2011.06.010
http://hdl.handle.net/11536/18364
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.06.010
期刊: APPLIED MATHEMATICS LETTERS
Volume: 24
Issue: 12
起始頁: 2115
結束頁: 2117
顯示於類別:期刊論文


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  1. 000294886000029.pdf