正規壓縮算子與正規延拓算子; Normal Compressions and Normal Dilations

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/7842

Title:	正規壓縮算子與正規延拓算子;Normal Compressions and Normal Dilations
Authors:	李佳萍;Chia-Ping Li
Contributors:	數學研究所
Keywords:	正規延拓算子;正規壓縮算子;Normal Compressions;Normal Dilations
Date:	2004-05-27
Issue Date:	2009-09-22 11:06:53 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	在此論文中，我們探討「正規壓縮算子」與「正規延拓算子」的性質。在「正規壓縮算子的數值域」（參考文獻８）中有如下的結果：『對於ｎ＋１階正規矩陣Ｎ的兩個ｎ階正規壓縮算子Ａ與Ｂ，Ａ與Ｂ么正等價，若且唯若，Ａ與Ｂ的所有特徵值都相同（包含重根）』。這篇論文的主要目地則是將上述結果推廣，並分成Ｎ是么正矩陣與Ｎ是正規矩陣兩種情形來探討。當Ｎ是么正矩陣時，Ａ與Ｂ么正等價，若且唯若，Ａ與Ｂ有超過半數的特徵值相同（包含重根）；當Ｎ是正規矩陣時，Ａ與Ｂ么正等價，若且唯若，Ａ與Ｂ有ｎ－１個特徵值相同（包含重根）。 In this thesis, we have two main results. First, we present the n-dimensional compressions of an (n+1)- dimensional unitary matrix are determined, up to unitary equivalence, by only half of their eigenvalues (counting multiplities). Second, we present the n-dimensional compressions of an (n+1)- dimensional normal matrix are determined, up to unitary equivalence, by their n-1 eigenvalues (counting multiplities).
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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