| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 葉鎮宇 | zh_TW |
| DC.creator | Zhen-Yu Ye | en_US |
| dc.date.accessioned | 2018-6-9T07:39:07Z | |
| dc.date.available | 2018-6-9T07:39:07Z | |
| dc.date.issued | 2018 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=105221018 | |
| 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 | 假設 A = [a_{ij}]_{i,j=1}^{n} 並且 A′ 是的加權移位矩陣的權重 a_{i,i+1} 對所有 i = 1,...,n
我們知道定理3.1 [1] 的 w(A) ≥ w(A′)。 在這篇論文中，我們考慮何時等式 w(A)= w(A)′ 成立。
在本論文中，我們得到了一些 w(A)= w(A′) 意味著 A = A′ 的矩陣A。 我們證明
(1) 如果 A 是一個非負矩陣，則 w(A)= w(A′) 若且唯若 A = A′，
(2) 如果 A 是一個 Toeplitz 矩陣，則 w(A) = w(A′) 若且唯若
A = A′，以及
(3) 如果 A 是循環矩陣，則 w(A)= w(A′)若且唯若 A = A′。
請注意，A′ 是一個加權移位。 如果 A′ 具有週期性非零權重，我們還考慮何時等式 w(A)= w(A′)
成立。 我們首先研究 A′ 的權重的週期是一。
給出了等式 w(A)= w(A′) 的充分必要條件。
接下來，我們關注 A′ 的權重的週期是偶數。 我們證明，如果
w(A)= w(A′)，那麼A是整體可分解的。 最後，本文還考慮了 A′ 的權重週期為奇數的情況。 | zh_TW |
| dc.description.abstract | Let A=[a_ij]_(i,j=1)^n and A′ be a weighted shift matrix of weights {a_i,i+1} for all i=1,...,n
We know that w(A)≥w(A′) by Proposition 3.1{1}. In this thesis, we consider when the equality w(A)=w(A′) holds. In this thesis, we obtain some classes of matrices A for which w(A)=w(A′) implies A=A′. We show that (1) if A is a non-negative matrix, then w(A)=w(A′) if and only if A=A′, (2) if A is a Toeplitz matrix, then w(A)=w(A′) if and only if A=A′, and (3) if A is a circulant matrix, then w(A)=w(A′) if and only if A=A′.
Note that A′ is a weighted shift. We also consider when the equality w(A)=w(A′) holds if A′ has periodic nonzero weights.
We first study the period of weights of A′ is one.
The sufficient and necessary condition of the equality w(A)=w(A′) is given.
Next, we concerned with the period of weights of A′ is even. We show that if w(A)=w(A′), then A is unitarily reducible. Finally, the case that the period of weights of A′ is odd is also considered in this thesis. | en_US |
| DC.subject | 數值半徑 | zh_TW |
| DC.subject | 矩陣 | zh_TW |
| DC.subject | Numerical radius | en_US |
| DC.subject | Matrices | en_US |
| DC.title | Numerical Radii of Matrices and its Submatrices | 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 |