Trace of matrix

👨🏻‍🏫 學術台數學

魏王將張遼

2008-12-15 5:39 am

For an n x n matrix A, the sum of the diagonal elements is called the trace:

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec08/Crazymat1.jpg

(a) Show that trace (AB) = trace (BA) where B is another n x n matrix.
(b) Deduce that: if A is similar to B, then trace (A) = trace (B)
In particular, if A is similar to diag (λ1, λ2, ..., λn), then

圖片參考：http://i117.photobucket.com/albums/o61/billy_hywung/Dec08/Crazymat2.jpg

回答 (4)

Jacob

2008-12-18 12:43 am

✔ 最佳答案

http://lrg103.zorpia.com/0/4945/31653147.2d1a12.jpg

2008-12-17 18:07:54 補充：
佢咁勁邊可能唔識。但佢既然咁問得，自然歡迎我作答。XD

2008-12-17 20:17:07 補充：
點解張遼兄而家唔做管理員啊？

參考: ME

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魏王將張遼

2008-12-18 3:25 pm

發問問題絕非只為尋求新知識, 若有自己所知者而又欲分享予眾人皆可發問.

此為末將上任分類管理員時官方所作的陳詞.

2008-12-18 07:26:39 補充：
我仍是管理員, 只係版面顯示不到.
去我個檔案頁就知.

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myisland8132

2008-12-18 2:04 am

EMK呀EMK﹐難道你認為飛天魏國大將軍張遼不懂

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Ivan

2008-12-16 10:49 am

呢條好 standard 的linear algebra 喎...

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