# 臺灣博碩士論文加值系統

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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
 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 ofmatrices, 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) 135-140.4. A. Condon and R.J.Lipton. On the complexity of space bounded interactive proof,Proceedings of the 30th Annual Symposium on Foundations ofComputer Science, Research Triangle Park, NC, 1989: 462-467.5. I. Daubechies and J.C. Largarias. Set of matrices all infinite products of which converge, Linear Algebra and it''s application 161(1992): 227-263.6. J.C. Largarias, and Y. Wang. The finiteness conjecture for the generalized spectral radius of a set of matrices, Linear Algebra and it''s application 214(1995): 17-42.7. G.-C. Rota and G. Strang. A note on the joint spectralradius, Indag. Math. 22(1960): 379-381. 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄    top
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