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April 11th, 2010, 10:48 PM   #1
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invariant subspace

Let T be a linear operator on a vector space with a T-invariant subspace W. Prove that if v is an eigenvector of T_w with corresponding eigenvalue ?, then the same is true for T.
proof:
T(v)=?v => T_w (v)=?v. implies that T = T_w.
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