Crawford numbers of powers of a matrix

Kuo Zhong Wang, Pei Yuan Wu, Hwa Long Gau

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

or 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 ∂W(A)). It is shown that if A has eigenvalues λ1,⋯, λn arranged so that |λ 1|≥⋯≥|λn|, then lim kc(Ak)1/k (resp., limkC(A k)1/k) equals 0 or |λn| (resp., |λj| for some j, 1≤j≤n). For a normal A, more can be said, namely, lim kc(A(Ak)1/k=|λn| (resp., limkC((Ak)1/k=|λj| for some j, 3≤j≤n). In these cases, the above possible values can all be assumed by some A.

原文???core.languages.en_GB???
頁(從 - 到)2243-2254
頁數12
期刊Linear Algebra and Its Applications
433
發行號11-12
DOIs
出版狀態已出版 - 30 12月 2010

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