[線代] basis, vector space
碰到一個問題想請教大家~~ 關於basis & vector space的~
題目給的訊息條件:
B : a basis for a real vector space V , dim(V)>1
有幾個問題想釐清:
1. 這裡的V是指所有實數可形成的vector space還是就是指實數R本身
2. 條件中特意強調了dim(V)>1, 除了暗示B的元素不只一個，
還有暗示其他的性質嗎？
3. 為什麼"there's a basis for V that is disjoint from B"是對的呢？
4. 為什麼 "B is a proper subset of a linearly independent subset of V"
是錯的？我覺得"proper"這個字眼有點讓這個敘述是錯的嫌疑，
但不懂為什麼....
謝謝大家!!
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