博碩士論文 102221016 詳細資訊




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姓名 林肯甫(Ken-fu Lin)  查詢紙本館藏   畢業系所 數學系
論文名稱 3×3矩陣乘積之數值域及數值域半徑
(NUMERICAL RANGES AND NUMERICAL RADII OF PRODUCTS OF 3×3 MATRICES)
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摘要(中) 在本篇論文中,對任意3×3的複數矩陣A和B,我們給出了充分且必要的條件對於AB矩陣乘積的數值域和BA矩陣乘積的數值域相等時。此外,去研究當A和A2的數值域半徑為1且A3的數值域半徑小於1時,A會有什麼樣的矩陣結構。以及最後,我們給出了充分且必要的條件對於當A為壓縮矩陣其特徵值長度皆小於1且A的範數為1,A與B張量積的數值域半徑等於A的範數與B的數值域半徑乘積時。
摘要(英) In this thesis, for any two 3-by-3 complex matrices A and B, we show that the necessary and sufficient conditions for the equality W(AB) = W(BA) to hold, where W() denotes the numerical range of a matrix, a nd the structure of A when w(A) =w (A2) = 1 and w (A3) < 1, where w() denotes the numerical radius of a matrix, and obtain the necessary and sufficient condition for the equality w(A B) = kAkw(B)to hold when A is a completely nonunitary contraction with kAk = 1, where k  k
denotes the usual operator norm of a matrix.
關鍵字(中) ★ 數值域
★ 數值域半徑
★ 張量積
★ 壓縮矩陣
關鍵字(英) ★ numerical range
★ numerical radius
★ tensor product
★ contraction
論文目次 Contents
1. Introduction 1
2. Preliminaries 4
2.1. Basic properties of numerical range and numerical radius 4
2.2. The Kippenhahn curve and polynomial 7
2.3. Contractions and Sn-matrices 10
2.4. Tensor product 12
3. Numerical ranges of products of 3  3 matrices 14
4. Numerical radii of powers of 3  3 matrices 24
5. Tensor products of 3  3 matrices 34
References 36
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3
指導教授 高華隆(Hwa-long Gau) 審核日期 2015-6-29
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