Re: [理工] [線代] 99台大電機
※ 引述《compulsory (まけない!)》之銘言：
: suppose that v,w,z are vector in R^n such that v is orthogonal to z and z is
: orthogonal to w. Then
: (a)For any orthogonal n*n matrix H,we have that Hz is orthogonal to both v & w
: (b)v+w is orthogonal to z
: (c)v is orthogonal to w
: (d)For any orthogonal n*n matrix H, we have that Hv is orthogonal to z
: 我知道b是對的
: c是錯的
: a d不太會選
a) 舉一個n = 2的情況為反例
let v = (1,0), z = (0,1), w = (2,0)
H = [ 0 1 ] Hz = (1,0) 並沒有和 v,w 正交
[ 1 0 ]
d) 我想是相同道理吧!
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