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數學系簡茂丁教授發表最新期刊論文

Reducibility of the ternary forms of unitary bordering matrices

(么正升階矩陣三元式的可約化性)

作者：Mao-Ting Chien, Hiroshi Nakazato

LINEAR ALGEBRA AND ITS APPLICATIONS

卷:527 頁碼:73-86，出版日期:2017年8月15日 (SCI)

摘要：

In this paper, necessary and sufficient conditions are presented for reducibility of the ternary forms associated to 3-by-3 unitary bordering matrices. A one-parameter family of n-by-n unitary bordering matrices is given for which its associated ternary form is the product of linear and quadratic forms for n less than or equals to 6. As a consequence, the higher rank numerical ranges of this family of unitary bordering matrices have elliptical boundaries.

在本文中，給出3-階么正升階矩陣關聯的行列式三元式可約化的充分必要條件，並且造一族n-階么正升階方陣使其行列式三元式可約化為線性與二次式的乘積。利用此結果，導出這一族么正升階矩陣的高秩數值域的邊界曲線都是橢圓。

關鍵字：

作者關鍵字:Unitary bordering matrices; Ternary forms; Reducibility; Numerical ranges

KeyWords Plus:BLASCHKE PRODUCTS; ELLIPSES; CURVES

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