| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 葉雅婷 | zh_TW |
| DC.creator | Ya-ting Yeh | en_US |
| dc.date.accessioned | 2011-5-31T07:39:07Z | |
| dc.date.available | 2011-5-31T07:39:07Z | |
| dc.date.issued | 2011 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=972201022 | |
| 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 | 本論文探討對角方塊都是零的2×2方塊矩陣的數值域。我們證明當B是k×k(k>2)矩陣滿足B*B是k-1維的單位矩陣和一維0矩陣的直和，則此2×2方塊矩陣其數值域會是兩個內切在[-1,1]×[-1,1]正方形裡的橢圓的凸包。另一方面，只要B滿足∥B∥=1，我們也對此2×2方塊矩陣其數值域的邊界給出刻劃。此外，對於4階的2×2方塊矩陣 ，我們也給出其數值域會是兩個內切在[-1,1]×[-1,1]正方形裡橢圓的凸包的充分必要條件。
| zh_TW |
| dc.description.abstract | In this thesis, we study the numerical range of a 2-by-2 block matrix with zero diagonal block. We show that if B∈M_(k−1,k) (k ≥ 3) satisfies BB*=I_(k−1), then the numerical range of the 2-by-2 block matrix is the convex hull of two ellipses inscribed in the square [−1, 1] × [−1, 1]. On the other hand, we also show that if B ∈ M_k (k ≥ 3) satisfies
∥B∥=1, then the numerical range of the 2-by-2 block matrix has 4 line segments on its boundary. Among other things, we consider the 2-by-2 block matrix A ∈ M_4, and we give a sufficient and necessary condition in terms of entries of B for numerical range of A being the convex hull of two ellipses.
| en_US |
| DC.subject | 方塊矩陣 | zh_TW |
| DC.subject | 三對角線矩陣 | zh_TW |
| DC.subject | 數值域 | zh_TW |
| DC.subject | Tridiagonal matrix | en_US |
| DC.subject | Numerical range | en_US |
| DC.subject | Block matrix | en_US |
| DC.title | 2×2方塊矩陣的數值域 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | Numerical Ranges of 2-by-2 Block Matrices | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |