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Math Help - Inner product space

  1. #1
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    Inner product space

    Show that in an inner product space, x perpendicular to y if and only if  ||x+\alpha y||\geqslant||x|| for all sclar  \alpha
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    For example, if the inner product space is real, express the inequality in the form \alpha(2<x,y>+\alpha||y||^2)\geq 0 .
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    Quote Originally Posted by geezeela View Post
    Show that in an inner product space, x perpendicular to y if and only if  ||x+\alpha y||\geqslant||x|| for all sclar  \alpha
    Sorry i meant to say
    Show that in an inner product space, x orthogonal to y if and only if  ||x+\alpha y||\geqslant||x|| for all sclar  \alpha
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by geezeela View Post
    Sorry i meant to say Show that in an inner product space, x orthogonal to y if and only if  ||x+\alpha y||\geqslant||x|| for all sclar  \alpha

    Many thanks for this information.
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    Re: Inner product space

    I need some help with this question...please guys help me....
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  6. #6
    MHF Contributor FernandoRevilla's Avatar
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    Re: Inner product space

    Quote Originally Posted by geezeela View Post
    I need some help with this question...please guys help me....
    What about the hint I gave you?
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