Re: [理工] [線代] 99台大電機

[christianSK (AG)]

※ 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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推 compulsory:感謝
→ BenLinus:用幾何的角度來想, orthogonal matrix 就是旋轉的意思,
→ BenLinus:轉個角度, 也許就不垂直了
推 hunter0904:正交保角度 Hv Hz就會垂直
→ dy957:樓上說的其實也是保內積
→ BenLinus:嗯嗯, 一起轉某個角度, 相對好像沒轉一樣。
推 mmkuo:哦哦~  所以這題如果說是Hv正交Hz的話就是Ture囉? 是嗎?
→ BenLinus:是的