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Unformatted text preview: 1 1 1 1 1 111 11 11 111 1 . 4. (Bonus Question) (a) Prove or give a counterexample: the product of any two selfadjoint operators on an innerproduct space is selfadjoint. (b) If T is a normal operator on a nitedimensional complex inner product space such that T 9 = T 8 prove that T is selfadjoint and T 2 = T . 5. (Bonus Question) (a) Let T be a linear operator on a vector space V such that dim(Im( T )) = n . Prove that T has at most n + 1 distinct eigenvalues. (b) If T is a linear operator on a vector space V such that any vector of V is an eigenvector of T prove that T is a scalar multiple of the identity operator....
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 Winter '06
 TOTH
 Algebra

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