Crawford numbers of powers of a matrix

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/51127

Title:	Crawford numbers of powers of a matrix
Authors:	Wang,KZ;Wu,PY;Gau,HL
Contributors:	數學系
Keywords:	VALUES
Date:	2010
Issue Date:	2012-03-27 18:22:33 (UTC+8)
Publisher:	國立中央大學
Abstract:	For an n-by-n matrix A, its Crawford number c(A) (resp., generalized Crawford number C(A)) is, by definition, the distance from the origin to its numerical range W(A) (resp., the boundary of its numerical range partial derivative W(A)). It is shown that if A has eigenvalues lambda(1), ..., lambda(n) An arranged so that vertical bar lambda(1)vertical bar >= ... >= vertical bar lambda(n)vertical bar, then (lim) over bar (k) c(A(k))(1/k) (resp., (lim) over bar (k) C(A(k))(1/k))equals 0 or vertical bar lambda(n)vertical bar (resp., vertical bar lambda(j)vertical bar for some j, 1 <= j <= n). For a normal A. more can be said, namely, (lim) over bar (k) c(A(k))(1/k) = vertical bar lambda(n)vertical bar (resp., (lim) over bar (k) C(A(k))(1/k) = vertical bar lambda(j)vertical bar for some j, 3 <= j <= n). In these cases, the above possible values can all be assumed by some A. (C) 2010 Elsevier Inc. All rights reserved.
Relation:	LINEAR ALGEBRA AND ITS APPLICATIONS
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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