### 博碩士論文 105221020 詳細資訊

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(Equality of Numerical Ranges of 4×4 Matrix Powers)

 ★ 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 ★ 四階方陣的高秩數值域 ★ 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

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★ 數值域

★ Numerical Ranges

Chapter 2. Preliminaries................................................................3
2.1 Basic properties of numerical range ................................. 3
2.2 Kippenhahn Curve..................................................4
Chapter 3. Equality of Numerical Ranges of 2 × 2 and 3 × 3 Matrices..................13
3.1 Equality of Numerical Ranges of 2 × 2 Matrices ................... 13
3.2 Equality of Numerical Ranges of 3 × 3 Matrices....................16
Chapter 4. Equality of Numerical Ranges of 4 × 4 Matrices............................26
References...............................................................44

[2] C.-T. Chang, H.-L. Gau, K.-Z. Wang, Equality of higher-rank numerical ranges of matrices, Linear Multilinear Algebra, 62 (2014) 626-638.
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[4] H.-L. Gau, K.-Z. Wang, P. Y. Wu, Euqality of Numerical Ranges of Matrix Powers, Linear Algebra Appl., to appear.
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[10] R. Kippenhahn, Uber den Wertevorrat einer Matrix, Math. Nachr., 6 (1951), 193-228.
[11] Y.-H. Liu, Elliptic Numerical Range of 4x4 matirces, Master’s thesis, National Central University, 2003.
44
[12] F. D. Murnaghan, On the field of values of a square matrix, Proc. Nat. Acad. Sci. U.S.A., 18 (1932), 246-248.
[13] S.-H. Tso, P. Y. Wu, Matrical ranges of quadratic operators, Rocky Mountain J. Math., 29 (1999) 1139-1152.
[14] P. Y. Wu, Numerical Ranges of Hilbert Space Operators, Cambridge University Press, Cambridge, to appear.