  博碩士論文 962201030 詳細資訊

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(Higher-Rank Numerical Ranges of 4-by-4 Matrices)

 ★ 橢圓形數值域之四階方陣 ★ 數值域邊界上之線段 ★ 正規壓縮算子與正規延拓算子 ★ 加權排列矩陣及加權位移矩陣之數值域 ★ 可分解友矩陣之數值域 ★ 可分解友矩陣之研究 ★ 關於巴氏空間上連續函數的近乎收斂性 ★ 三角不等式與Jensen不等式之精化 ★ 缺陷指數為1的矩陣之研究 ★ A-Statistical Convergence of Korovkin Type Approximation ★ I-Convergence of Korovkin Type Approximation Theorems for Unbounded Functions ★ 位移算子其有限維壓縮算子的反矩陣 ★ 2×2方塊矩陣的數值域 ★ 加權位移矩陣的探討與廣義三角不等式的優化 ★ 喬登方塊和矩陣的張量積之數值域半徑 ★ 3×3矩陣乘積之數值域及數值域半徑

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★ 高秩數值域(Higher-Rank Numerical Range)
★ Kippenhahn Curve

★ Higher-Rank Numerical Range
★ Numerical Range

2 Preliminaries --2
2.1 Basic properties for numerical ranges --2
2.2 Kippenhahn curve --4
2.3 Higher-rank numerical ranges --5
2.4 Numerical ranges and higher-rank numerical ranges of 3 × 3 Matrices --8
3 Higher-Rank Numerical Ranges of 4 × 4 Matrices --9
3.1 Four linear factors --11
3.2 Two linear factors and a quadratic irreducible factor --13
3.3 Two quadratic irreducible factors --16
3.4 A linear factor and a cubic irreducible factor --18
3.5 \$p_A\$ is irreducible --35
References --37

 M.D. Choi, J.A. Holbrook, D. W. Kribs, K. Yczkowski, Higher-rank numerical ranges of unitary and normal matrices, Operators and Matrices, 1 (2008), 409-426.
 M.D. Choi, D. W. Kribs, K. Yczkowski, Higher-rank numerical ranges and compression problems, Linear Algebra Appl. 418 (2006), 828-839.
 R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge Univ. Press, 1985.
 D.S. Keeler, L. Rodman and I.M. Spitkovsky, The numerical range of 3 × 3 matrices, Linear Algebra Appl. 252 (1997), 115-139.
 F. Kirwan, Complex Algebraic Curves, Cambridge Univ. Press, 1992.
 C.K. Li, Y.T. Poon, N.S. Sze, Condition for the higher rank numerical range to be non-empty, Linear and Multilinear Algebra, in press, preprint, http://arxiv.org/abs/0706.1540.
 C.K. Li, N.S. Sze, Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations, Proc. Amer. Math. Soc. 136 (2008), 3013-3023.
 H.J. Woerdeman, The higher rank numerical range is convex, Linear and Multilinear Algebra, 56 (2008), 65-67.
 P.Y. Wu, Numerical Ranges of Hilbert Space Operators, preprint.