| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 彭煜釗 | zh_TW |
| DC.creator | Yu-Jhau Peng | en_US |
| dc.date.accessioned | 2009-6-17T07:39:07Z | |
| dc.date.available | 2009-6-17T07:39:07Z | |
| dc.date.issued | 2009 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=962201030 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.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。
| zh_TW |
| dc.description.abstract | 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.
| en_US |
| DC.subject | 數值域(Numerical Range) | zh_TW |
| DC.subject | 高秩數值域(Higher-Rank Numerical Range) | zh_TW |
| DC.subject | Kippenhahn Curve | zh_TW |
| DC.subject | Kippenhahn Curve | en_US |
| DC.subject | Higher-Rank Numerical Range | en_US |
| DC.subject | Numerical Range | en_US |
| DC.title | 四階方陣的高秩數值域 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Higher-Rank Numerical Ranges of 4-by-4 Matrices | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |