  博碩士論文 93221015 詳細資訊

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(A Study on 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 ★ 可分解友矩陣之數值域 ★ 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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。令*1 1 rank( ) 1 kI −AA =* =
2 2 rank( ) 1 n k I AA − − { : rank( * )=1 and | | , ( )} n n Sα ≡ A∈M I−AA λ =α ∀λ ∈σ A
，則相當於1 是屬於A k Sα 且2 是屬於A 1/
n k S α
− 。亦證明每一個屬於n Sα

；(c)
1 W(A)=W(A)
1 1) n 2 n1 W(J ) W(A − ⊆ W(A ) W(J ) − ⊆ 。

Furthermore, we show that the following statements are equivalent:
(a) W(A)=W(A_1); (b)W(J_{n-1})subseteq W(A_1); (c)W(A_2)subseteq W(J_{n-1}).

★ numerical range

2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Basic Properties of Numerical Range . . . . . . . . . . .3
2.2 Companion Matrices . . . . . . . . 4
3. The S^alpha_n Matrices . . . . . . .6
4. Reducible Companion Matrices . . . . . . .21
References . . . . . . .29

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