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請問主軸定理畫圖題的那個新的軸為什麼是eigenspace
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lin801011
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Jan 8, 2014, 8:21:12 AM
1/8/14
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請問為啥u軸就是v(25) v軸就是v(0)
林立宇
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Jan 8, 2014, 12:50:03 PM
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要想想看我們當初怎麼擺旋轉矩陣P出來的噢
P = [v1 v2], 其中v1, v2皆為A的eigenvectors
因為橢圓在兩軸上的向量在新座標形式一定是y1 = s(1, 0)及y2 = t(0, 1), for some s, t
所以將兩軸上的向量擺回舊座標看, 因為x = Py,
所以y1的舊座標x1 = Py1 = P(s[1 0]^t) = s*v1
同理y2的舊座標x2 = Py2 = P(t[0 1]^t) = t*v2
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