作者PttFund (批踢踢基金只进不出)
看板Math
标题[线代] 线代(1)
时间Sat Jul 23 18:38:02 2005
Let V be a subspace of R^n. A linear transformation
μ: R^n -> R^n is called a projection of R^n on V if
μ(x) in V and x-μ(x) in V^⊥ for every x in R^n.
(a) Let A be a n╳n matrix. Show that μ: R^n -> R^n
defined by μ(x) = Ax for all x in R^n is a projection
of R^n onto C(A), if and only if A^2 = A and A = A^T.
(C(A) = the column space of A.)
(b) What are the eigenvalues and the corresponding
eigenspaces of a projection?
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