作者mqazz1 (無法顯示)
看板Math
標題[線代] one-to-one and onto
時間Sat May 14 22:25:30 2011
let D be the differentiation operator on P[3], and let
S = {p屬於P[3] | p(0)=0}
show that
(a) D maps P[3] onto the subspace P[2], but
D: P[3] -> P[2] is not one-to-one
(b) D: S -> P[3] is one-to-one but not onto
請問這題該怎麼證呢?
謝謝!!
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1F：→ ricestone :(a)P[3]裡面每個只差常數的多項式都會映到同一個 05/14 22:35
2F：→ ricestone :(b)P[2]中任一元素都可以積分回去唯一的P[3]元素 05/14 22:37
3F：→ ricestone :上一行說錯了 05/14 22:39
4F：→ ricestone :(b)S中任兩不同元素經過映射後會射到不同兩點 05/14 22:41
5F：→ ricestone :(b)可以用兩式相減來證 05/14 22:42
6F：推 aegius1r :Kernel, image 05/14 22:43
7F：→ ricestone :不過你從以前到現在問了這麼多線代問題，到了現在還 05/14 22:45
8F：→ ricestone :問這類題目還蠻怪的... 05/14 22:45
9F：→ recorriendo :樓上+1 從以前就看到你問類似的題目了 05/15 00:21