查詢結果分析
來源資料
相關文獻
- Rayleight Quotient and Orthogonal Transformation
- Sequential Eigenstructure Assignment with Minimal State-Feedback Gain
- Sequential Eigenstructure Assignment with Maximal Stability Robustness
- 以大衛生演算法建構之三維爐心擾動計算方法
- The Analysis & Recongnition between Noise and Chaos on the Laser System
- Orthogonal Framework for Linear Prediction Analysis
- Torsional Vibration Suppression by Excitation Control of Synchronous Motor Driving Mass-Spring Load Systems
- Analysis of Robust Eigenvalue--Clustering in a Ring for Linear Uncertain Discrete Time-Delay Systems
- Vibration and Elastic Instability of a Gun Drilling Shaft
- 同心圓環二維Helmholtz特徵方程問題真假根探討
頁籤選單縮合
題 名 | Rayleight Quotient and Orthogonal Transformation=Rayleigh商與正交轉換 |
---|---|
作 者 | 簡燦榮; | 書刊名 | 蘭陽學報 |
卷 期 | 4 2005.05[民94.05] |
頁 次 | 頁177-182 |
分類號 | 313.3 |
關鍵詞 | Rayleigh商; Hermitian矩陣; 特徵值; 正交轉換; Rayleigh quotient; Hermitian matrix; Eigenvalues; Orthogonal transformation; |
語 文 | 英文(English) |
中文摘要 | Rayleight原則(請參考[1], 頁6-101.[2], 頁 416~427)宣稱:在歐幾里得n度空間中,(n>0), 任一個Hermitian短陣A的Rayleight 商 R(v)=<A(v),v>/<v,v>一定會有極大值、極小值. 而且分別正是A短陣的特徵值中的極大值、極小值。本文則利用Rayleight商證明:在歐幾里得n度空間中, (n>0), 任一個線性轉換A的Rayleight商 R(v)=<A(v),v>/<v,v>也一定會有極大值、極小值。並且利用Rayleight商的微分證明:任一個正交轉換至少會有一個一維或二維的不變子空間。 |
英文摘要 | In [1], p.6-101, [2], pp.416~427, Rayleigh principle announces that the Rayleigh quotient R(v)=<A(v),v>/<v,v> of a Hermitian matrix A in Euclidean space of dimension n, □, (n>0), attains its maximum and minimum just to be the maximum and minimum of the eigenvalues of A respectively. In this paper, we want to show how the Rayleigh quotient of any linear transformation A in □, (n>0), attains its maximum and minimum. We also use the quotient to prove that an orthogonal transformation A has at least an invariant subspace of dimension 1 or2, by suing the differentiability of the Rayleigh quotient. |
本系統中英文摘要資訊取自各篇刊載內容。