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Math Help - Euclidean vector space

  1. #1
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    Euclidean vector space

    Show that for two vectors v and w of a Euclidean vector space V we have |v+w| ≤ |v|+ |w|.

    Can anybody help with this please?
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  2. #2
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    Quote Originally Posted by jackiemoon View Post
    Show that for two vectors v and w of a Euclidean vector space V we have |v+w| ≤ |v|+ |w|.

    Can anybody help with this please?
    First you will need the cauchy-schwarz inequality <v,w> \le |v||w|

    Now starting with the square we get


    |v+w|^2=<v+w,v+w>=<v,v>+<w,w>+2<v,w> \le
    |v|^2+|w|^2+2|v||w|=(|v|+|w|)^2

    Now we take the square root and we are done.
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