※ 引述《mqazz1 (无法显示)》之铭言： : Every n*n matrix has n eigenvalues and n eigenvectors : False : ======== : (d) Each eigenvector of A is also an eigenvector of A^2 : True 2 2 Av ＝ λv => A v ＝ A(Av) ＝ A(λv) ＝ λ(Av) ＝ λ v. v: eigenvector. : (e) Each eienvector of an invertible matrix A is also : an eigenvector of A^(-1) : True Note that if A is invertible, then 0 is not an eigenvalue of A. -1 -1 -1 Av ＝ λv => v ＝ A (Av) ＝ A (λv) ＝ λ(A v) -1 -1 => A v ＝ λ v. v : eigenvector, λ: eigenvalue. : (f) If v is an eigenvector of an invertible matrix A, : then cv is an eigenvector of A^(-1) for all nonzero scalars c : True -1 -1 -1 -1 -1 -1 Av ＝ λv => A v ＝ λ v => A (cv) ＝ c(A v) ＝ c(λ v) ＝ λ (cv). v : eigenvector, λ: eigenvalue. : 请问这些是为什麽? : 谢谢 -- ▁▂▁ ︵-●-● ▲╯╰▲ 英雄 英雄 胆小狗英雄 ▼ ▲ 小笨狗! 嗷呜~ ∫˙ ˙ +╮ 从小就被抛弃 你害我好丢脸! ╲ =◣◢= ╱ 是茉莉儿好心把他捡回来 ▁ ▼◣ ╱ ╪╪╪ ︴ 他帮助茉莉儿夫妇解决困难 ▅◣ ◣ ▲ ︴ --

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