Don't know how to prove the following, thanks for help.
Suppose a is a vector with the property that a.b=0 for every vector b. Prove that we must have a=0.
Thank you very much!
Vector proof
2009-10-09 3:09 pm
回答 (3)
2009-10-09 5:05 pm
✔ 最佳答案
Please refer to the followings:圖片參考：http://i726.photobucket.com/albums/ww265/physicsworld2010/physicsworld01Oct090902.jpg?t=1255050292
參考: Physics king
2009-10-14 1:26 pm
只要 inner product space 都對，並不需要假設 R^n。
題目中也沒有說要假設 finite dimension。
問的人要說清楚，你的架構是在 inner product space。有時候甚至要說明是 real 還是 complex inner product space。如下列命題：
V complex inner space, T: V--> V linear and (Tx, x) = 0 for all x in V, then T = 0, the zero operator.
complex 換成 real 就不行。
題目中也沒有說要假設 finite dimension。
問的人要說清楚，你的架構是在 inner product space。有時候甚至要說明是 real 還是 complex inner product space。如下列命題：
V complex inner space, T: V--> V linear and (Tx, x) = 0 for all x in V, then T = 0, the zero operator.
complex 換成 real 就不行。
2009-10-09 9:15 pm
Since a.b = 0 holds true for all b, then this is also true for b = a => a.a = 0
=> | a |^2 = 0 => a = 0
=> | a |^2 = 0 => a = 0
收錄日期: 2021-04-19 15:56:16
原文連結 [永久失效]:
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