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Math Help - inner product by A is the same as the standard inner product on R^n

  1. #1
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    Question inner product by A is the same as the standard inner product on R^n

    The Question is as follows

    inner product by A is the same as the standard inner product on R^n-lin-alg.jpg

    Please some on help I really don't know how to do this one.

    Thank you in advanced
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  2. #2
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    Re: inner product by A is the same as the standard inner product on R^n

    what you "probably" mean by the inner product induced by A is:

    <u,v> = (Au)T(Av).

    if AAT = I, then AT = A-1, so ATA = I, as well. thus:

    <u,v> = (Au)T(Av) = (uTAT)(Av) = uT(ATA)v = uTv = u.v
    Thanks from ohYeah
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  3. #3
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    Re: inner product by A is the same as the standard inner product on R^n

    You have really done me a great favor by helping me with my two questions
    thank You
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