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http://ir.lib.ncu.edu.tw/handle/987654321/51127
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| 題名: | Crawford numbers of powers of a matrix |
| 作者: | Wang,KZ;Wu,PY;Gau,HL |
| 貢獻者: | 數學系 |
| 關鍵詞: | VALUES |
| 日期: | 2010 |
| 上傳時間: | 2012-03-27 18:22:33 (UTC+8) |
| 出版者: | 國立中央大學 |
| 摘要: | 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. |
| 關聯: | LINEAR ALGEBRA AND ITS APPLICATIONS |
| 顯示於類別: | [數學系] 期刊論文
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