[理工] [線代] 請問一個 Vector space 問題

[kb2011 (ming)]

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

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◆ From: 220.133.139.27
→ caribouR:第一個就把所有的條件都檢查一次即可
→ caribouR: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
推 da0910cc:r的地方可以用那8個性質去證明
→ da0910cc:C的地方:可以取N=2,a=i,v=(1,0)
→ da0910cc:av=(i,0) 不屬於R^2 不等於女優