### 博碩士論文 90221012 詳細資訊

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(Line Segments of The Boundary of Numerical Range)

 ★ 橢圓形數值域之四階方陣 ★ 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 ★ 3×3矩陣乘積之數值域及數值域半徑

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In this case, we will give a sufficient and necessary condition for the numerical range of a 4 by 4 matrix with a line segment on its boundary. Moreover, we also give a criterion for
the numerical range of a 4 by 4 matrix with a pair of parallel line segment on its boundary.

2. Preliminaries
2.1 Basic Properties of Numerical Range
2.2 Kippenhahn Curve
3. The Numerical Range of 3 by 3 Matrices
4. The Numerical Range of 4 by 4 Matrices
4.1 A is reducible
4.2 pA is reducible
4.3 pA is irreducible
Reference

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Math. Nachr., 6 (1951),193-228.
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Matrices, Sci.Rep. Hirosaki Univ., 43(1996),209-221.
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Operators, preprint.