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研究生:呂明杰
研究生(外文):Ming-Jiea Liu
論文名稱:UndecidabilityofFinitenessConjectureforgeneralizedspectralradius
論文名稱(外文):Undecidability of Finiteness Conjecture for generalized spectral radius
指導教授:施茂祥
指導教授(外文):Mau-Shiang Shih
學位類別:碩士
校院名稱:國立臺灣師範大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:18
中文關鍵詞:Undecidability of Finiteness Conjecture for generalized spectral radius
外文關鍵詞:Undecidability of Finiteness Conjecture for generalized spectral radius
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The generalized spectral radius ( ) of a set complex matrices is ( ) =
, where = sup{ ( ): each }. The main object of this paper is to study the following problems. Finiteness Conjecture: For each
finite set of n n complex matrices, there is some finite k such that
( ) = . Effective Finiteness Conjecture: For any finite set of n n matrices with rational entries, there is some finite k such that ( ) = .
Question: Are the Finiteness Conjecture and the Effective Finiteness Conjecture true? Via the undecidability of the Effective Finiteness Conjecture, we show that the answer to the Finiteness Conjecture is negative.
The generalized spectral radius ( ) of a set complex matrices is ( ) =
, where = sup{ ( ): each }. The main object of this paper is to study the following problems. Finiteness Conjecture: For each
finite set of n n complex matrices, there is some finite k such that
( ) = . Effective Finiteness Conjecture: For any finite set of n n matrices with rational entries, there is some finite k such that ( ) = .
Question: Are the Finiteness Conjecture and the Effective Finiteness Conjecture true? Via the undecidability of the Effective Finiteness Conjecture, we show that the answer to the Finiteness Conjecture is negative.
Content
1. Introduction………………………………………………2
2. Undecidability Problem………………………………………3
3. Undecidability of Effective Finiteness Conjecture…8
4. Disproof of Finiteness Conjecture……………………8
5. Normed Finiteness Conjecture……………………………9
6. Normed Finiteness Conjecture for Euclidean Norm……11
7. Application of Theorem 6.1…………………………16
8. A Research Problem…………17
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