作者superconan (超级柯南)
看板Math
标题[线代] eigenvalue eigenvector & projection & reflection
时间Sun Jun 5 00:36:51 2011
What are the eigenvalues and eigenvectors of a projection ? A reflection ?
目前我知道投影矩阵 P = A(A^TA)^(-1)A^T 且 P^2 = P
Let t is an eigenvalue of P and v is an eigenvector of P, then Pv = tv. — (1)
Pv = P^2v = P(Pv) = P(tv) = t(Pv) = t(tv) = t^2v. — (2)
By (1), (2) => t^2 = t => t^2 - t = 0 => t(t-1) = 0 => t = 0, 1
其他的就不知道怎麽求了
麻烦高手解惑，谢谢～
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1F：推 recorriendo :你可以用几何观点来想 投影矩阵的值域只有1维 06/05 01:05
2F：→ superconan :请问「投影矩阵的值域只有1维」是一定的吗？ 06/05 02:52
3F：→ superconan :还是说是因为现在Pv = tv，投影矩阵把v变成tv是1维？ 06/05 02:54
4F：→ superconan :我还是不知道怎麽求投影矩阵的eigenvectorsˊˋ 06/05 02:55
5F：→ yhliu :1F 是错的! 06/05 03:14