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研究生:李佳萍
研究生(外文):Chia-Ping Li
論文名稱:正規壓縮算子與正規延拓算子
論文名稱(外文):Normal Compressions and Normal Dilations
指導教授:高華隆
指導教授(外文):Hwa-Long Gau
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:92
語文別:英文
論文頁數:24
中文關鍵詞:正規壓縮算子正規延拓算子
外文關鍵詞:Normal CompressionsNormal Dilations
相關次數:
  • 被引用被引用:0
  • 點閱點閱:101
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  • 下載下載:6
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摘 要

論文名稱:正規壓縮算子與正規延拓算子
頁數:24頁
畢業時間及提要別:九十二學年度第二學期碩士論文提要
研究生:李佳萍       指導教授:高華隆
論文提要內容:  
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).
Normal Compressions and Normal Dilations

Contents

Chapter 1. Introduction …………………………………………………..1

Chapter 2. Notations and Preliminaries ………………………………….3
2.1 Unitary Compressions …………………………………..3
2.2 Normal Compressions …………………………………. 6

Chapter 3. Compression and Dilation ……………………………………11
3.1 Compression……………………………………………. 11
3.2 Dilation ………………………………………………….16

References………………………………………………………………….. 23
References
(1) M. Adam, J. Maroulas, On compressions of normal matrices, Linear Algebra Appl. 341 (2002) 403--418.
(2) U. Daepp, P. Gorkin, R. Mortini, Ellipses and finite Blaschke products, Amer. Math. Monthly 109 (2002) 785--795.
(3) K. E. Gustafson, D. K. M. Rao, Numerical Range, the Field of Values of Linear Operators and Matrices, Springer, New
York, 1997.
(4) H.-L. Gau, P. Y. Wu, Numerical range of $S(phi)$, Linear and Multilinear Algebra 45 (1998) 49--73.
(5) H.-L. Gau, P. Y. Wu, Dilation to inflations of $S(phi)$, Linear and Multilinear Algebra 45 (1998) 109--123.
(6) H.-L. Gau, P. Y. Wu, Lucas' theorem refined, Linear and Multilinear Algebra 45 (1998) 359--373.
(7) H.-L. Gau, P. Y. Wu, Numerical range and Poncelet property, Taiwanese J. Math. 7 (2003) 173--193.
(8) H.-L. Gau, P. Y. Wu, Numerical range of a normal compression, Linear and Multilinear Algebra. 52 (2004) 195--201.
(9) H.-L. Gau, P. Y. Wu, Numerical range of a normal compression II , Linear and Multilinear Algebra, to appear.
(10) H.-L. Gau, P. Y. Wu, Numerical range circumscribed by two polygons, Linear Algebra Appl. 382 (2004) 155--170.
(11) Halmos, P. R.,A Hilbert space problem book, 2nd end., Springer-Verlag, New York. (1982)
(12) R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge, 1991.
(13) B. Mirman, V. Borovikov, L. Ladyzhensky, R. Vinograd, Numerical ranges, Poncelet curves, invariant measures,
Linear Algebra Appl. 329 (2001) 61--75.
(14) B. Mirman, P. Y. Wu, Matrix interpretation of Marden's proof of Siebeck's theorem,
preprint.
(15) B. Mirman, Numerical ranges and Poncelet curves, Linear Algebra Appl. 281 (1998) 59--85.
(16) B. Mirman, UB-matrices and conditions for Poncelet polygon to be
closed, Linear Algebra Appl. 360 (2003) 123--150.
(17) P. Y. Wu, Polygons and numerical ranges, Amer. Math. Monthly 107 (2000) 528--540.
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