矩陣的對角化

DESCRIPTION

矩陣的對角化. (Diagonalization of Matrices). 對角矩陣. 非對角線元素均為零之矩陣. 可對角化的矩陣. A 為 n n 階矩陣，若存在另一 n n 階非奇異矩陣 P 使 P − 1 AP 為一對角矩陣，則稱 A 為可對角化矩陣. 當此 P 存在時，稱 P 可對角化 A. 若 A 為 n n 階矩陣，其 n 個特徵值為  1 、 2 、、 n ，且各別所對應的特徵向量為 e 1 、 e 2 、 、 e n ，則. 或改寫成. P. P. D. 令. 及. 則.

Download

1 / 18

Mar 18, 2014

Télécharger la présentation

矩陣的對角化

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

矩陣的對角化 (Diagonalization of Matrices)
對角矩陣 非對角線元素均為零之矩陣
可對角化的矩陣 A為nn階矩陣，若存在另一nn階非奇異矩陣 P 使 P−1AP 為一對角矩陣，則稱 A 為可對角化矩陣. 當此P 存在時，稱 P 可對角化 A.
若A為nn階矩陣，其 n 個特徵值為 1、2、、n，且各別所對應的特徵向量為e1、e2、、en，則
或改寫成 P P D
令及則對角化完成！
[例題] A的特徵值為1, 3 其對應的特徵向量分別為

[例題]
上式明顯有一根為1

二者必須 線性獨立

(有2個任意常數)
二者必須線性獨立

More Related