博碩士論文 952201009 詳細資訊

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(A Study on Matrices of Defect Index One)

 ★ 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 ★ 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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norm of \$mathcal{S}_n^{-1}\$-matrices in terms of its eigenvalues.

★ 缺陷指數
★ 極分解

★ numerical range
★ defect index

2. Preliminaries .........................................2
2.1 Basic Properties of Numerical Range...................2
2.2 Matrices of Defect Index One..........................3
2.3 Matrices of Classes \$S_n\$ and \$S_n^{-1}\$..............3
2.4 Polar Decompositions of \$S_n\$-Matrices ...............4
3. Main Results...........................................5
3.1 Classifications of Matrices of Defect Index One.......5
3.2 Polar Decompositions of \$S_n^{-1}\$-Matrices...........8
3.3 Matrix Representations for Operators in \$S_n^{-1}\$...12
3.4 Numerical Ranges of \$S_n^{-1}-Matrices...............17
3.5 Norm of \$S_n^{-1}\$ -Matrices.........................29
• References ............................................31

[2] R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.
[3] D.S.Keeler, L. Rodman and I.M. Spitkovsky, The Numerical Range of 3×3 Matrices, Linear Algebra and its Appl., 252 (1997), 115–139.
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[9] M.-S. Sun, A Study on Reducible Companion Matrices, Master Thesis, June 2006, National Central University, Taiwan.