| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 林肯甫 | zh_TW |
| DC.creator | Ken-fu Lin | en_US |
| dc.date.accessioned | 2015-6-29T07:39:07Z | |
| dc.date.available | 2015-6-29T07:39:07Z | |
| dc.date.issued | 2015 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=102221016 | |
| 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 | 在本篇論文中，對任意3×3的複數矩陣A和B，我們給出了充分且必要的條件對於AB矩陣乘積的數值域和BA矩陣乘積的數值域相等時。此外，去研究當A和A2的數值域半徑為1且A3的數值域半徑小於1時，A會有什麼樣的矩陣結構。以及最後，我們給出了充分且必要的條件對於當A為壓縮矩陣其特徵值長度皆小於1且A的範數為1，A與B張量積的數值域半徑等於A的範數與B的數值域半徑乘積時。 | zh_TW |
| dc.description.abstract | In this thesis, for any two 3-by-3 complex matrices A and B, we show that the necessary and sufficient conditions for the equality W(AB) = W(BA) to hold, where W() denotes the numerical range of a matrix, a nd the structure of A when w(A) =w (A2) = 1 and w (A3) < 1, where w() denotes the numerical radius of a matrix, and obtain the necessary and sufficient condition for the equality w(A B) = kAkw(B)to hold when A is a completely nonunitary contraction with kAk = 1, where k k
denotes the usual operator norm of a matrix. | en_US |
| DC.subject | 數值域 | zh_TW |
| DC.subject | 數值域半徑 | zh_TW |
| DC.subject | 張量積 | zh_TW |
| DC.subject | 壓縮矩陣 | zh_TW |
| DC.subject | numerical range | en_US |
| DC.subject | numerical radius | en_US |
| DC.subject | tensor product | en_US |
| DC.subject | contraction | en_US |
| DC.title | 3×3矩陣乘積之數值域及數值域半徑 | zh_TW |
| dc.language.iso | zh-TW | zh-TW |
| DC.title | NUMERICAL RANGES AND NUMERICAL RADII OF PRODUCTS OF 3×3 MATRICES | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |