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研究生:奈賓薩
研究生(外文):Binsar Tulus Nainggolan
論文名稱:三對角代數正矩陣之性質
論文名稱(外文):Tridiagonal Algebraically Positive Matrix
指導教授:王雅書
指導教授(外文):Ya-Shu Wang
口試委員:蔡明誠陳中川
口試委員(外文):Tsai Ming-ChangChung-Chuan Chen
口試日期:2020-01-06
學位類別:碩士
校院名稱:國立中興大學
系所名稱:應用數學系所
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:2020
畢業學年度:108
語文別:中文
論文頁數:28
中文關鍵詞:符號矩陣代數正性質
外文關鍵詞:Algebraic PositivitySign Pattern
相關次數:
  • 被引用被引用:0
  • 點閱點閱:76
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  • 下載下載:6
  • 收藏至我的研究室書目清單書目收藏:0
本論文中,我們說明了具有代數正性質的nxn 三對角矩陣為符號對稱矩陣,
其中,n = 3; 4; 5。
Algebraically positive matrix was introduced by Kirkland, Qiao, and Zihan in 2006. A square matrix A with real entries is said to be algebraically positive if there exists a polynomial f such that all the entries of the matrix f (A) are positive. In this thesis, we show that if an nxn tridiagonal matrix is algebraically positive then its corresponding sign pattern is symmetric, here n = 3, 4, and 5.
1. Introduction 1
2. Preliminary 4
3. Correction 8
4. Tridiagonal Algebraically Positive Matrix 20
References 28
[1] S. kirkland, P. Qiau and X. Zhan, Algebraically positive matrices, Linear Algebra and its Applications, 504(2016),14{26.
[2] X. Zhan, Matrix Theory, GSM 147, Amer. Math. Soc., Providence, RI, 2013.
[3] S. Das and S. Bandopadhyay, On some sign patterns of algebraically positive, Linear Algebra and its Application, 562(2019), 91{122.
[4] Y.-S. Wang and L. F. Simanjuntak, 4 4 tridiagonal symmetric sign patterns which allow or require algebraic positivity, NCHU Master Thesis (2018).
[5] J. L. Abagat and D. C. Pelejo, "On Sign Pattern Matrices that Allow or Require Algebraic
Positivity", Electronic Journal of Linear Algebra, 35, 331{356.
[6] R. A. Brualdi and B. L. Shader, Matrices of Sign-solvable Linear Systems, Cambridge Uni-
versity Press, Cambridge, 1995.
[7] P. A. Samuelson, Foundations of Economic Analysis, Harvard Univer- sity Press, Cambridge,
Mass., 1947; New York, 1971.
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