Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/98471
標題: 3x3 符號對稱的代數正矩陣之結構
3x3 Symmetric Sign Patterns which Allow or Require Algebraic Positivity
作者: 希德溫
Citra Dewi Hasibuan
關鍵字: 符號矩陣;代數正性質;Sign Pattern;Algebraic Positivity
摘要: 
本論文中,我們探討了具有代數正性質的 3x3 符號對稱的符號矩陣。分別刻
劃了此類型 3x3 符號矩陣要求(require) 及允許(allow) 代數正性質的符號矩陣
表現式。

A sign pattern matrix (or sign pattern) is a matrix with entries in the set $left { +,-, 0
ight }$. For a real matrix $B$, $sgn(B)$ is the matrix obtained by replacing each positive (respectively, negative, zero) entry of $B$ with + (respectively, -, 0). A square real matrix $A$ is said to be algebraically positive if there exists a real polynomial $f$ such that $f(A)$ is a positive matrix. A sign pattern $mathcal{A}$ is said to require $mathcal{P}$ if every real matrix $B$ with $sgn(B)=mathcal{A}$ has property $mathcal{P}$; A sign pattern $mathcal{A}$ is said to allow $mathcal{P}$ if exists a real matrix $B$ with $sgn(B)=mathcal{A}$ has property $mathcal{P}$. In this thesis, we characterize $3 imes 3$ symmetric sign patterns which require or allow algebraic positivity.
URI: http://hdl.handle.net/11455/98471
Rights: 同意授權瀏覽/列印電子全文服務,2020-08-10起公開。
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