- 學位論文
Undecidability of Finiteness Conjecture for generalized spectral radius
Undecidability of Finiteness Conjecture for generalized spectral radius
若您是本文的作者，可授權文章由華藝線上圖書館中協助推廣。
摘要
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.
並列摘要
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.
參考文獻
1. T. Ando, M.H. Shih. Simultaneous contractibility,
SIAM J. Matrix Anal. Appl. 19(2)1998: 487-498.
2. M.A. Berger and Y. Wang. Bounded semigroup of
matrices, Linear Algebra and it's application. 166(1992): 21-27.
3. V.D. Blondel and J.N. Tsitiklis. The boundedness of all products of pair of matrices is undecidable, System and Control Letters. 41(2000) 135-140.