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Math Help - orthogonal matrix...

  1. #1
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    Post orthogonal matrix...

    Hello I need help in this matrix problem. I know it seems pretty simple but I am having hard time proving it..

    Let U E M(nxn) (C) be a unitary matrix, that is UU*=U*U=I. Let A, X be eigenpair for U. Prove that |A| = 1

    ---This is what I have got. So please tell me if I need to add something or is it completely wrong approach. Thanks for the kind help!

    Let U be the unitary matrix...
    then, Suppose x is an eigenvector corresponding to the eigenvalue λ of U. Then Ux = λx, so
    ||Ux|| = ||λx|| = |λ| . ||x||
    But U preserves lengths, so ||Ux|| = ||x||, and hence |λ| = 1....Do I have to give the reason why U preserves lengths?? and how??
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  2. #2
    A Plied Mathematician
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    Only you know if you need to include in the proof that orthogonal matrices preserve lengths. If you do need to prove that, then consider



    and so on.
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