| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 李佳穎 | zh_TW |
| DC.creator | Lee Chia Ying | en_US |
| dc.date.accessioned | 2019-6-12T07:39:07Z | |
| dc.date.available | 2019-6-12T07:39:07Z | |
| dc.date.issued | 2019 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=105221020 | |
| 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 | 探討當W(A) 與 W(A^k) 相等，對於所有 1 ≤ k ≤ n + 1。我們根據方陣A的unitary-similarity-invariant結構來尋找A的條件。
我們首先呈現當2×2矩陣A再一次到三次時W(A)皆相等，若且唯若A為冪等(idempotent)。則當3×3矩陣A在一次到四次時W(A)皆相等，若且唯若A么正相似(unitarily similar)於2×2冪等方正B與矩陣C的直和，且矩陣C滿足W(C^k) ⊆ W(B) 對於所有 1 ≤ k ≤ 4。我們的對於4×4矩陣的主結果將延續這個方向進行討論。
| zh_TW |
| dc.description.abstract | In this thesis, we are interested in the question of when $W(A)$ equals $W(A^k)$ for all $1le kle n+1$. We look for conditions in terms of the unitary-similarity-invariant structure of $A$. We show that if $A$ is $2 imes 2$, then $W(A)=W(A^k)$ for all $1le kle 3$ if and only if $A$ is idempotent. We also show that if $A$ is $3 imes 3$, then $W(A)=W(A^k)$ for all $1le kle 4$ if and only if $A$ is unitarily similar to a direct sum of the form $Boplus C$, where $B$ is a $2 imes 2$ idempotent and $C$ satisfies $W(C^k)subseteq W(B)$ for all $1le kle 4$. Our main results are the analysis of $4 imes 4$ matrices along this line. | en_US |
| DC.subject | 矩陣 | zh_TW |
| DC.subject | 數值域 | zh_TW |
| DC.subject | Matrix | en_US |
| DC.subject | Numerical Ranges | en_US |
| DC.title | Equality of Numerical Ranges of 4×4 Matrix Powers | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |