可約伴同矩陣的數值域之研究;A Study on the Numerical Ranges of Reducible Companion Matrices

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/57041

Title:	可約伴同矩陣的數值域之研究;A Study on the Numerical Ranges of Reducible Companion Matrices
Authors:	高華隆
Contributors:	中央大學數學系
Keywords:	數學類
Date:	2009-09-01
Issue Date:	2012-10-01 15:10:19 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	本計畫中，我們想要知道可約伴同矩陣是否會被其數值域所完全決定。相當於，我們想要證明兩個n乘n可約伴同矩陣若有相同的數值域，則他們必為相同矩陣。因此，我們將會對可約伴同矩陣的直和子作細部的研究。另一方面，我們也對那些具有橢圓盤數值域的可約伴同矩陣，給出完整的刻劃與判別的準則。 ; In this project, we want to know whether reducible companion matrices are completely determined by its numerical range. That is, we want to show that two n-by-n reducible companion matrices with same numerical range are equal to each other. We will give a detailed study on the properties of direct summands of reducible companion matrices. On the other hand, we also want to obtain a criterion for a reducible companion matrix to have an elliptic numerical range ; 研究期間 9808 ~ 9907
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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