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Math Help - what am i doing wrong on this problem please help

  1. #1
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    what am i doing wrong on this problem please help

    let T:V -> V denote an isometry on V, where V is a real inner product space.
    prove that the eigenvalues corresponding to different eigenvectors of T are orthogonal.

    here is what i did.
    let v1, v2 be eigenvectors corresponding to eigenvalues u1, u2 respectively.
    since T is an isometry on V, <T(v1) T(v2)> = <v1 v2>.
    and
    <T(v1) T(v2)> = <u1v1 u2v2> = u1u2<v1 v2> = <u1 u2>
    so u1u2<v1 v2>-<v1 v2> = 0
    (u1u2-1)<v1 v2> = 0

    how do i show that u1u2-1 does not equal 0 or this is not at all correct?
    please help.
    Last edited by Kat-M; January 8th 2009 at 03:07 PM.
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  2. #2
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    The eigenvalues for such mapping can only be \pm 1.
    Thus u_1u_2 = -1
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