### 博碩士論文 92221004 詳細資訊

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(Numerical Ranges of Reducible Companion 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 ★ 3×3矩陣乘積之數值域及數值域半徑

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In Section 3, 4 × 4 reducible companion matrices will be completely solved. We show that a 4 × 4 reducible companion matrix A has an ellipse as its numerical range if and only if either σ(A)＝{a,-a,i/a,-i/a} where |a|≧sqrt(1+sqrt(2)), or σ(A)＝{a,ai,-1/a,-i/a} where |a|≧1+sqrt(2). Here σ(A) denotes the spectrum of the matrix A. In Section 4, we discuss the cases for 6 × 6 reducible companion matrices.

★ 友矩陣
★ 數值域

★ Reducible
★ Numerical Range

2. Preliminaries.................................................3
2.1 Basic Properties of Numerical Ranges.....................3
2.2 Reducible Companion Matrices.............................6
3. 4 × 4 Reducible Companion Matrices............................9
4. 6 × 6 Reducible Companion Matrices...........................16
‧References...................................................20

[2] U.Haagerup, P. de la Harpe, The numerical radius of a nilpotent operator on a Hilbert space, Proc. Amer. Math. Soc. 115 (1992) 371–379.
[3] R. A. Horn and C. R. Johnson. Matrix analysis, Cambridge University Press, Cambridge, 1985.
[4] R. A. Horn and C. R. Johnson. Topics in matrix analysis, Cambridge University Press, Cambridge, 1991.
[5] D. S. Keeler, L. Rodman and I. M. Spitkovsky, The numerical range of 3 × 3 matrices, Linear Algebra Appl., 252 (1997), 115–139.