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 Scope All of NCUIR 理學院    數學研究所       --博碩士論文 Tips: please add "double quotation mark" for query phrases to get precise resultsplease goto advance search for comprehansive author search Adv. Search
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 Please use this identifier to cite or link to this item: `http://ir.lib.ncu.edu.tw/handle/987654321/7971`

 Title: 四階方陣的高秩數值域;Higher-Rank Numerical Ranges of 4-by-4 Matrices Authors: 彭煜釗;Yu-Jhau Peng Contributors: 數學研究所 Keywords: 數值域(Numerical Range);高秩數值域(Higher-Rank Numerical Range);Kippenhahn Curve;Kippenhahn Curve;Higher-Rank Numerical Range;Numerical Range Date: 2009-06-02 Issue Date: 2009-09-22 11:10:32 (UTC+8) Publisher: 國立中央大學圖書館 Abstract: 本論文探討一個四階方陣A，其高秩數值域的幾何圖形是什麼樣的圖形。我們將四階方陣的秩二數值域分類。對於一個四階方陣A，我們經由考慮A的associated polynomial來對秩二數值域作分類。對於每一個分類，我們將完整地描述它們的幾何圖形。 Let \$A\$ be an \$n\$-by-\$n\$ matrix. For \$1leq k leq n\$, the rank-\$k\$ numerical range of \$A\$ is defined and denoted by \$Lambda_k(A) = {lambdainmathbb{C}: PAP=lambda P mbox{ for some rank-{it k} orthogonal projection \$P\$}}\$. In this thesis, we give a complete description of the higher-rank numerical ranges of \$4\$-by-\$4\$ matrices. We classify the rank-\$2\$ numerical ranges of \$4\$-by-\$4\$ matrices. Our classification is based on the factorability of the associated polynomial \$p_A(x,y,z)equiv mathrm{det}(xmathrm{Re,}A + ymathrm{Im,}A + zI_4)\$ of a \$4\$-by-\$4\$ matrix \$A\$. For each class, we also completely determine the shape of the rank-\$2\$ numerical range of a \$4\$-by-\$4\$ matrix. Appears in Collections: [數學研究所] 博碩士論文

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