標題: 友矩陣和規範算子的數值域
Numerical Ranges of Companion Matrices and Normal Operators
作者: 陳育慈
Yu-Tzu Chen
吳培元
Pei-Yuan Wu
應用數學系所
關鍵字: 數值域;規範算子;友矩陣;numrrical range;normal operator;companion matrix
公開日期: 2006
摘要: 在本篇論文中,我們研究兩類算子的數值域。針對友矩陣部分,我們證明 可分解友矩陣的數值域會包含相對應的 友矩陣的數值域的充要調件為 可分解友矩陣的行列式值的絕對值會大於1。然而,相對應的結果在一般的 可分友矩陣並不正確。針對規範算子的部份,我們將數值域以乘積算子的表現函數來表示。
In this thesis, we study the numerical ranges of two kinds of operators. For companion matrices, we show that the numerical range of a 3-by-3 reducible companion matrix C(p) contains the numerical range of the 2-by-2 companion matrix C((1=3)p0) if and only if the absolute value of its determinant is greater than 1. However, the corresponding assertion for n-by-n reducible companion matrices is false. For a normal operator, we express its numerical range in terms of the function in its multiplication operator representation.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009422520
http://hdl.handle.net/11536/81301
Appears in Collections:Thesis


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