推 wolf0000:那span(ψ)={0}的0是代表0元素還是0向量呢???我搞混了= = 01/28 15:33
→ wolf0000:所以如果題目是問說W1∩W2 =span(ψ)，是成立嗎? 01/28 15:33
→ privatewind:true, 直和的兩個子空間 就是這樣 01/28 17:22
→ cha122977:zero vector 01/28 17:46
推 wolf0000:瞭解了!!感謝大家的回應!! 01/28 18:15
※ 引述《wolf0000 (小狼)》之銘言：
: Let V be a vector space,and W1 and W2 be two subspace of V.
: Is it possible that the intersection of W1 and W2, W1∩W2 = ψ,
: where ψ denotes the empty set.
: 解答是說因為W1跟W2為向量子空間，所以零向量都包含在W1跟W2裡，
: 所以零向量屬於W1跟W2的交集， 故W1∩W2 = ψ不可能成立。
: 前面的觀念我都懂...但是empty set它裡面的元素不就是零嗎?
No... empty set is just empty,there `s nothing.
But zero element means the identity
such like 0 for addition,1 for multiplication.
So,two of the W1 and W2 have zero element if they are subspace of V.
W1∩W2 != ψ
: 為什麼有零向量不是empty set??? 這邊觀念有點模擬~"~
: 肯請高手解惑! 感謝:)
ps. span(ψ)={0}
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 219.71.209.172