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。 Appears in Collections: 應用數學系所