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| 研究生： |
呂明杰 Ming-Jiea Liu |
|---|---|
| 論文名稱： |
Undecidability of Finiteness Conjecture for generalized spectral radius Undecidability of Finiteness Conjecture for generalized spectral radius |
| 指導教授： |
施茂祥
Shih, Mau-Shiang |
| 學位類別： |
碩士 Master |
| 系所名稱： |
數學系 Department of Mathematics |
| 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 |
| 英文關鍵詞： | Undecidability of Finiteness Conjecture for generalized spectral radius |
| 論文種類： | 學術論文 |
| 相關次數： | 點閱：179 下載：1 |
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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.
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