[理工] [線代] 請問一個 Vector space 問題

看板Grad-ProbAsk作者 (ming)時間14年前 (2011/07/16 11:36), 編輯推噓1(104)
留言5則, 2人參與, 最新討論串1/1
課本上的問題, 不知道答案為什麼是這樣?? Let V = {(a1, a2, ...,an):ai E C} is a vector space Is V a vector space over the field of real numbers with the operations of coordinatewise addition and multiplication? Ans: Yes Let V = {(a1, a2, ...,an):ai E R} is a vector space Is V a vector space over the field of complex numbers with the operations of coordinatewise addition and multiplication? Ans: No 請高手幫忙解惑, 感謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 220.133.139.27

07/16 11:45, , 1F
第一個就把所有的條件都檢查一次即可
07/16 11:45, 1F

07/16 11:45, , 2F
第二個V裡的東西作用一個C裡的常數不一定還會掉在R裡
07/16 11:45, 2F

07/16 15:33, , 3F
r的地方可以用那8個性質去證明
07/16 15:33, 3F

07/16 15:35, , 4F
C的地方:可以取N=2,a=i,v=(1,0)
07/16 15:35, 4F

07/16 15:36, , 5F
av=(i,0) 不屬於R^2 不等於女優
07/16 15:36, 5F
文章代碼(AID): #1E8GSkbU (Grad-ProbAsk)