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(Solved):   Problem 38. Suppose that T is a normal operator on V and that 3 and 4 are eigenvalues of T ...



Problem 38. Suppose that T is a normal operator on V and that 3 and 4 are
eigenvalues of T. Prove that there exists a vector

 

Problem 38. Suppose that T is a normal operator on V and that 3 and 4 are eigenvalues of T. Prove that there exists a vector v € V such that ||v|| = ?2 and ||Tv|| = 5. [10 marks] im


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The important result on normal operator to be used is: Theorem: For a normal operator A, eigenvectors co
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